Universal dynamical control of quantum mechanical decay Modulation of the coupling to the c
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弱测量在提高量子参数估计精度中的应用刘丽君【摘要】Quantum metrology concerns how to achieve the highest precision of physical parameters by quantum re-sources, which has broad applications in many fields. For closed quantum systems, the accuracy attained with entangled quantum probes can significantly surmount that of classical strategies. However, when noises such as decoherence are tak-en into account, the quantum gain may be jeopardized. In this paper, weak measurement is adopted to improve estimation precision in the presence of amplitude-damping decoherence, and it is demonstrated that the method of weak measurement can recover estimation precision to the Heisenberg limit, even though the success probability is in a exponential attenuation. Furthermore, the effectiveness of weak measurement in improving the estimation precision is investigated when ancillary systems are implemented.%量子参数估计理论主要研究如何利用量子资源来提高经典参数的估计精度,其应用非常广泛.对于封闭的量子系统,采用纠缠的量子探针测量未知的经典参数,其估计精度可以大幅地超越经典探针所能达到的精度.然而,当退相干效应存在时,量子探针的优越性就会受到限制.本文引入弱测量的方法提高噪声环境下参数估计的精度,并证明了当退振幅噪声存在时,这一方法可以使得参数估计的精度恢复到海森堡极限,尽管实现的概率会随着探针个数的增加呈指数地减少.本文进一步考察了当辅助系统存在时,弱测量的方法对提高参数估计精度的有效性.【期刊名称】《控制理论与应用》【年(卷),期】2017(034)011【总页数】6页(P1471-1476)【关键词】量子参数估计;弱测量;精度极限【作者】刘丽君【作者单位】山西师范大学数学与计算机科学学院,山西临汾041000【正文语种】中文【中图分类】O5621 引言(Introduction)量子参数估计理论,即利用量子资源提高经典参数的估计精度,在实际中的应用非常广泛,如引力波探测[1–2]、原子钟[3–5]、原子磁强计[6–8]以及原子自旋陀螺仪[9–10]等.典型的量子参数估计过程主要分为4个部分:1)制备初态已知的量子系统作为探针;2)探针与参数系统进行相互作用;3)对含有未知参数的量子系统进行测量;4)利用测量数据以及适当的方法构造待测参数的估计值.由于估计值和真实值之间会存在误差,量子参数估计理论(也称为量子度量学)的主要任务是从理论上刻画估计误差的界以及达到误差下界的具体操作方法.对于量子参数估计,参数的真实值与估计值之间的误差依赖于实验过程中制备的初态.已有的文献[11–12]已经证明,对于封闭的量子系统,利用纠缠的量子资源,参数估计的精度可以超越经典探针所达到的标准量子极限(即估计误差的下界与成正比),实现海森堡极限(即估计误差的下界与1/N成正比),其中N为实验中探针的个数.当非线性的相互作用存在时,参数估计的精度甚至可以超越海森堡极限[13].然而,当量子系统在演化过程中不可避免地与环境发生相互作用时,参数估计的精度最终会退化到标准量子极限[14–16].因此,如何采取有效的方法等效地抑制量子系统的退相干、提高参数估计的精度极限成为进一步迫切需要解决的问题.针对量子系统的退相干效应,目前已经提出了很多有效的方法进行抑制,例如量子纠错码(quantum error correction)[17–19]、消相干子空间(decoherence-free subspace)[20–21]、动态解耦(dynamical decoupling)[22]以及量子反馈控制(quantum feedback control)[23]等,这些方法为研究如何提高参数估计的精度极限提供了重要的理论参考.一些方法在提高参数估计精度方面的有效性已经被证明.例如,文献[24]中证明了当退相位噪声存在时,量子纠错码可以使得频率(以及相位)估计的精度极限恢复到海森堡极限.事实上,退相干效应的存在之所以会抑制量子参数的估计精度,其主要原因在于这一效应破坏了探针之间的量子关联.文献[25–28]中证明了采用弱测量的方法可以有效地抑制单比特的退振幅(amplitude-damping)噪声,保护量子态的纠缠,而且其有效性已经在超导相位比特以及光子比特中得到了实验验证.本文将这一方法应用到参数估计中,考察当退振幅噪声存在时,这一方法在提高参数估计精度方面的有效性.在本文的方法中,两个弱测量过程会被加入到典型的估计过程中:第1个弱测量加在步骤2之前,这一过程可视为对初态做了一个选择;第2个弱测量加在步骤2之后,即对演化后的态再进行一次选择.经过这两次的选择,可选出仍然保持高度纠缠的态来进行进一步的参数估计.本文将会证明,利用这一方法,参数估计的精度可以恢复到海森堡极限.然而,经过两次弱测量过程,最终选择出来的满足要求的态的概率较低,且初态探针个数越多,成功概率就越低.在典型的量子参数估计过程中加入辅助的量子系统,这一方法也被证明了可以用来提高含退相干影响的参数估计精度[29].具体过程为:首先,探针与辅助系统处于一个纠缠的初态;其次,探针和系统共同经历动态演化.在此过程中,只有探针在待测参数的影响下进行演化,辅助系统不与参数系统相互作用.最后,对探针和辅助系统进行一个联合的测量,并根据测量数据以及适当的方法对待测参数进行估计.本文将引入辅助系统并与弱测量过程相结合,考察当辅助系统存在时,采用弱测量的方法是否能够进一步提高退振幅噪声影响下的参数估计的精度.2 参数估计的一般理论(General parameter estimation theory)本节主要介绍一般的参数估计理论,从而根据这一理论来进一步分析当退振幅噪声存在时,弱测量过程对参数估计精度的影响.假设实验中未知的参数为x,其估计值xest与真实值之间的误差可由均方根误差δx 来刻画:其中〈·〉是对所有的测量结果取平均.对于任意的局部无偏估计方法,均方根误差δx满足量子Cram´er-Rao不等式:其中:ρ(x)为以ρ0为初态的探针在参数系统的作用下演化后的末态,ν为实验独立重复的次数,FQ为量子Fisher信息量,刻画了在最优的测量策略下,从实验中可提取的关于未知参数的最大信息量,通常定义为其中:厄密算子Lρ称为密度算子ρ的对称对数导数(symmetric logarithmic derivative),算子ρ′为密度算子ρ关于参数x求导数,且满足方程特别地,如果将ρ做谱分解,记为则量子Fisher信息量可以表示为[29]由方程(1)可知,通过计算具体的量子Fisher信息量FQ的值,可以详细地分析不同的初态以及演化过程对参数估计精度的影响.首先考虑无噪声影响的频率估计情形.假设待估计的频率为ω,系统演化的哈密顿量为H.此时初态为ρ0的量子系统在参数及哈密顿量联合驱动下的演化是幺正的,可记为其中Uω=e−iωHt.根据典型的度量学方法,可以证明其中〈·〉0≡Tr(ρ0·).特别地,考虑局部哈密顿量H=其中为仅作用在第i个粒子上的Pauliσz算子.如果N个探针的初态为直积态,如其中|0〉和|1〉为σz的本征态.此时,参数估计的误差满足即所谓的标准量子极限.如果N个探针的初态为纠缠态,例如GHZ态:则参数估计的误差满足即所谓的海森堡极限.由此可知,对于完全封闭的系统,采用量子资源作为探针,参数估计的精度可以大幅地超越经典探针(直积态)所能达到的精度.事实上,对于一个实际的量子系统,总会不可避免地与环境发生相互作用,从而导致量子系统的退相干.大量的文献[15–16]已经证明,当退相干效应存在时,无论如何选择探针的初态,参数估计的精度都只能实现标准量子极限.量子效应仅使得参数估计的精度增强了一个常数倍.因此,如何有效地抑制退相干效应,恢复海森堡极限是一个亟待解决的问题.在下文中,将分析退振幅噪声对参数估计的影响,并证明弱测量可以提高参数估计精度的极限.3 退振幅噪声下的精度极限(Precision limit in the presence of amplitude damping noise)考虑典型的参数估计过程.初始的量子系综中包含N个二能级量子系统,整个系综演化的哈密顿量为其中ω为待估计的频率.当退振幅噪声以相同的比率γ局部地作用在每个量子系统上时,整个系综的演化可以描述为其中为Pauli阶梯算子(Pauli ladder operator),只作用在第i个二能级系统上.根据量子Cram´er-Rao不等式(1),为了分析ω的估计精度极限,需要求解末态ρ(t)来计算量子Fisher信息量.由于密度矩阵ρ(t)的维数随着探针个数N的增加呈指数增长,因此直接根据方程(3)求解末态ρ(t)是非常困难的,本文中将利用算子和的方法来表示ρ(t).由方程(3)可知,每个粒子的演化都是独立且相同的,其演化可由一个量子操作E来表示.若包含N个二能级量子系统的系综的初态为ρ0,则整个系综的末态ρ(t)可解析地表示为量子操作E的表达式可由方程(3)在N=1时得到,具体可以表示为上式为单个二能级系统演化的算子和表示,每个算子分别为其中算子与哈密顿量驱动下的动态演化相关.算子E1与E2与退振幅噪声有关,具体形式为其中b=e−2γt.在第2节中已经证明,对于无噪声影响的频率估计(即γ=0),若初态为GHZ态,则参数估计的精度可以实现海森堡极限.然而,当存在退振幅噪声时(即γ/=0),参数估计的精度会由海森堡极限退化到标准量子极限.具体地,当初态为GHZ态时,式(4)中密度矩阵对应的量子Fisher信息量可由式(2)计算且可以表示为经过一些简单的运算,可以证明这就意味着参数估计的精度退化到了标准量子极限.因此,为了保持量子资源在参数估计中的优越性,需要应用有效的方法等效地抑制量子系统的退相干.4 量子弱测量(Quantum weak measurement)退振幅噪声的存在,之所以会降低参数估计的精度,是因为它破坏了量子探针之间的量子关联.因此,提高参数估计精度的一个可能的方法是维持量子探针之间的纠缠.文献[26]中证明了,利用弱测量的方法可以保护量子态的纠缠.本文将这一方法引入到参数估计中,即在典型的参数估计方法中加入两个额外的弱测量过程,整个的操作过程如图1所示.前弱测量M1作用在探针进行动态演化之前,后弱测量M2作用在探针进行动态演化之后,每个弱测量以相同的强度作用到每个探针上.弱测量算子M1和M2分别取为其中pa和pc分别表示两个弱测量的强度.如果pa=pc=0,则M1和M2退化为单位矩阵,对整个的测量过程没有影响.此时,视为没有弱测量过程,即为典型的参数估计过程.为了下文中书写方便,记1−pa=a以及1−pc=c,且有0<a,c<1.图1 含弱测量的参数估计过程Fig.1 Parameter estimation protocol with weak measurements假定整个系综的初始状态为ρ0,下面将具体地分析每个阶段系统的状态.首先,对系综做前弱测量,即测量算子M1独立地作用到每个探针上.如果所有探针都得到对应M1的测量结果,则整个系综的状态变为然后,系统以状态ρ1进入到动态演化阶段.在哈密顿量驱动以及退振幅的作用下演化t时间后,系统的状态变为接下来,对系统的态ρ2进行后弱测量.如果所有探针都得到对应M2的测量结果,则整个系综的态ρ(t)可以记为注意到在整个测量过程中,进一步的演化(或测量)依赖弱测量得到的测量结果.如果测量结果是对应弱测量算子的,这样的态会被保留,否则将被丢弃.因此,整个过程的成功概率是小于1的.在实际的实验中,得到目标态(6)的概率为假设实验过程中成功地得到了末态(6),下面将证明这一态对应的参数估计精度可达到海森堡极限.具体地,取原子系综的初态为GHZ态,则对于末态(6),量子Fisher信息量可以表示为由方程(8),可以得到两个特殊的结果.首先,考虑a=c=1的情况,即不考虑弱测量方法.此时,量子Fisher信息可以退化为方程(5)中的其次,考虑c/a=1情形,即前弱测量与后弱测量的测量强度相同.此时量子Fisher信息可以简化为当c< 1时,显然有由此说明利用弱测量确实可以提高参数估计的精度.为了进一步分析弱测量方法可以提高参数估计精度的程度,本文对式(8)中的进行详细的分析.为了书写方便,记cN/aN=x,c(1−b)=y.在实际实验中,显然有x,y>0.从而,可以简写为其中函数f表示为函数f依赖变量x和y.因此,要得到的最大值需要求解f关于x和y的最小值.在实际的实验中,测量强度pa和pc是独立的,即a和c是独立的,因此可以将f关于x和y独立地进行优化.本文中首先对x进行优化,其次对y进行优化.由式(10)知,函数f在处取得最小值,且最小值为其中k=y/b,且k是大于0的.易知f(k)是随着k增加的函数,k越小,f(k)的值越小.当k足够小时,可以将f(k)近似为特别地,当2Nk≪1时,即k≪1/(2N),则近似地有f(k)≈4.因此,可知由此说明利用弱测量的方法,可以将参数估计的精度由标准量子极限恢复到海森堡极限.两个弱测量的测量强度也都与k有关,当k给定时,测量强度值得注意的是,在整个测量过程中加入的两个弱测量过程,会限制精度恢复到海森堡极限的概率.由方程(7)计算可知,成功概率为成功概率依赖于探针个数以及弱测量的强度.由于弱测量强度0<a,c<1,成功概率会随着比特数N增加呈指数衰减.当N足够大时,成功概率P趋近于0.事实上,如果将k看做是一个可调的变量,量子Fisher信息关于变量k是单调递减的(因为f(k)是随着k增加的函数),而成功概率P是随着k单调增加的(由于a和c是关于k 单调增加的),可以在二者之间取一个折中,既可以减小噪声对参数估计精度的影响,又可以提高成功的概率.无论如何,尽管以牺牲成功概率为代价,但是确实得到了参数估计的一个更好的精度,为抑制退相干提高参数估计的精度提供了一个切实可行的方法.5 辅助系统(Ancillary systems)在典型的量子参数估计过程中加入辅助的量子系统,这一方法已经在文献[29]中被证明对提高含退相干影响的参数估计精度是有帮助的.本文这一部分的内容将具体地分析当辅助系统存在时,弱测量过程能否进一步提高退振幅噪声影响下的参数估计的精度.具体操作过程如图2所示,在图(a)中,只对原系统进行弱测量操作;在图(b)中,辅助系统与原系统同时经过弱测量过程.图2 包含辅助系统和弱测量的参数估计过程Fig.2 Parameter estimation protocol with ancillary systems and weak measurements假定N个原系统的二能级量子系统与M个辅助的二能级量子系统构成初始的状态为ρSA.整个系统经过图2(a)中的操作过程后,如果每次弱测量的结果都恰好对应弱测量算子,则整个系统的末态为其中算子M1,M2,E仅作用在原系统的N个粒子上.由于弱测量操作的存在,得到这个末态的成功概率也是小于1的.引入辅助的量子系统后,原则上,辅助系统与原系统可构成任意形式的初态,本文只考虑初态为GHZ态的情形,即其中n=N+M为系统中所有量子子系统的总数.当整个系统的初态为GHZ态时,对于末态(13),量子Fisher信息量可以表示为特别地,当a=c=1时,即不加入弱测量过程时,量子Fisher信息量退化为显然有大于说明引入辅助系统确实可以增强退振幅噪声影响下的参数估计的精度.这一结果与文献[29]中的结果是一致的.此外,的表达式中并不包含M的值,由此说明,只要辅助系统存在,参数估计的精度就可以提高,但增加辅助的个数并不能进一步提高参数估计的精度.当0<a,c<1时,比较方程(8)和(14)可知,即证明了当辅助系统存在时,加入弱测量过程可以进一步提高参数估计的精度.如果M个辅助的二能级量子系统与原系统一起经历弱测量过程,整个系统经过图2(b)中操作过程后,如果每次弱测量的结果都恰好对应弱测量算子,则以ρSA为初态的整个系统的末态为当整个系统的初态为GHZ态,则对应的量子Fisher信息量可以表示为比较和可知,若取c/a作为一个独立的变量,则对于这一变量,和可达到的最大值是相同的.然而,的结果可以通过调节c/a的值,在对应的操作过程中实现且更易实验实现.因此,将辅助系统同时经历弱测量过程,对进一步提高参数估计的精度没有任何的帮助.总之,利用辅助系统与加入弱测量过程相结合,是可以进一步提高参数估计的精度,尽管这一提高也是概率性的.6 结论(Conclusions)本文主要证明了量子弱测量在提高参数估计精度方面的有效性.对于退振幅噪声,这一方法甚至可以将参数估计精度由标准量子极限恢复到海森堡极限.但是,弱测量过程对态的选取是概率性的,因此利用文中的方法提高参数估计精度的成功概率比较低,且随着探针个数的增加,成功概率呈指数地衰减.因此,为了将这一方法更好地应用到实际中,需要研究一些有效的方法来进一步提高成功概率,例如选取其他更一般的弱测量算子或者将量子弱测量与其他方法(如动态解耦[30]或量子反馈[31])相结合等.此外,我们还证明了当辅助系统存在时,利用弱测量方法可以进一步提高参数估计的精度.本文中选取的辅助系统和原系统耦合的初态为GHZ态,然而这个态并不一定是使得量子Fisher信息量达到最大的初态.对于更一般的初态,辅助系统及弱测量方法对提高参数估计精度的有效性,还需要进一步的证明.参考文献(References):【相关文献】[1]ZHAN C,JU L,DEGALLAIX J,et al.Parametric instabilities and their control in advanced interferometer gravitational-wave detectors[J].Physical Review Letters,2005,94(12):121102.[2]AASI J,ABADIE J,ABBOTT B P,et al.Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light[J].Nature Photonics,2013,7(8):613 – 619. [3]BAUCH A. Caesium atomic clocks: function, performance andapplications[J].Measurement Science and Technology,2003,14(8):1159.[4]BORREGAARD J,SØRENSEN A S.Near-Heisenberg-limited atomic clocks in the presence of decoherence[J].Physical Review Letters,2013,111(9):090801.[5]HUNTEMANN N,LIPPHARDT B,TAMM CHR,et al.Improved limit on a temporal variation ofmp/mefrom comparisons of Yb+and Cs atomic clocks[J].Physical ReviewLetters,2014,113(21):210802.[6]BUDKER D,ROMALIS M.Optical magnetometry[J].Nature Physics,2007,3(4):227 – 234.[7]DANG H B,MALOOF A C,ROMALIS M V.Ultrahigh sensitivity magneticfield and magnetization measurements with an atomic magnetometer[J].Applied Physics Letters,2010,97(15):151110.[8]WICKENBROCK A,TRIC¸OT F,RENZONI F.Magne tic induction measurements using an all-optical 87Rb atomic magnetometer[J].Applied Physics Letters,2013,103(24):243503. [9]COOPER J J,HALLWOOD D W,DUNNINGHAM J A.Entanglement-enhanced atomic gyroscope[J].Physical Review A,2010,81(4):043624.[10]FANG J,QIN J.Advances in atomic gyroscopes:a view from inertial navigation applications[J].Sensors,2012,12(5):6331 – 6346.[11]GIOVANNETTI V,LLOYD S,MACCONE L.Quantum metrology[J].Physical Review Letters,2006,96(1):010401.[12]GIOVANNETTI V,LLOYD S,MACCONE L.Advances in quantum metrology[J].NaturePhotonics,2011,5(4):222 – 229.[13]NAPOLITANO M,KOSCHORRECK M,DUBOST B,et al.Interaction-based quantum metrology showing scaling beyond the Heisenberg limit[J]//Nature,2011,471(7339):486 – 489.[14]ESCHER B M,DE MATOS FILHO R L,DAVIDOVICH L.General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology[J].NaturePhysics,2011,7(5):406 –411.[15]KOŁODY´NSKI J,DEMKOWICZ-DOBRZA´NSKI R.Efficient tools for quantum metrology with uncorrelated noise[J].New Journal of Physics,2013,15(7):073043.[16]LIU L,CHENG S,QI B,et al.Precision limit of atomic magnetometers in the presence of spin-destruction collisions[J].Journal of Physics B:Atomic,Molecular and Optical Physics,2015,48:035502.[17]KNILL E,LAFLAMME R,VIOLA L.Theory of quantum error correction for generalnoise[J].Physical Review Letters,2000,84(11):2525.[18]REEDMD,DICARLOL,NIGGSE,etal.Realizationofthree-qubit quantum error correction with superconducting circuits[J].Nature,2012,482(7385):382 – 385.[19]NIGG S E,GIRVIN S M.Stabilizer quantum error correction toolbox for superconducting qubits[J].Physical Review Letters,2013,110(24):243604.[20]XUE P,XIAO Y F.Universal quantum computation in decoherencefree subspace with neutral atoms[J].Physical Review Letters,2006,97(14):140501.[21]LIANG Z T,DU Y X,HUANG W,et al.Nonadiabatic holonomic quantum computation in decoherence-free subspaces with trapped ions[J].Physical Review A,2014,89(6):062312.[22]KHODJASTEH K,LIDAR D A,VIOLA L.Arbitrarily accurate dynamical control in open quantum systems[J].Physical Review Letters,2010,104(9):090501.[23]YUAN H,FUNG C H F.Optimal feedback scheme and universal time scaling for Hamiltonian parameter estimation[J].Physical Review Letters,2015,115(11):110401. [24]DR W,SKOTINIOTIS M,FRWIS F,et al.Improved quantum metrology using quantum error correction[J].Physical Review Letters,2014,112(8):080801.[25]KOROTKOV A N,KEANE K.Decoherence suppression by quantum measurement reversal[J].Physical Review A,2010,81(4):040103.[26]KIM Y S,LEE J C,KWON O,et al.Protecting entanglement from decoherence using weak measurement and quantum measurement reversal[J].Nature Physics,2012,8(2):117 –120.[27]HE Z,YAO C,ZOU J.Improvement of entanglement transfer by weak measurement and quantum measurement reversal in two parallel Heisenberg spin chains[J].Journal of Physics B:Atomic,Molecular and Optical Physics,2014,47(4):045505.[28]LI W,HE Z,WANG Q.Protecting distribution entanglement for twoqubit state usingweak measurement and reversal[J].International Journal of TheoreticalPhysics,2017,56:2813–2824.[29]HUANG Z,MACCHIAVELLO C,MACCONE efulness of entanglement-assisted quantum metrology[J].Physical Review A,2016,94(1):012101.[30]XU K,LINPENG X Y,WANG Z L.Decoherence suppression combining quantum uncollapsing and dynamical decoupling[J].Applied Physics Letters,2014,104(26):263509.[31]WANG C Q,XU B M,ZOU J,et al.Feed-forward control for quantum state protection against decoherence[J].Physical Review A,2014,89(3):032303.。
A SINGLE PC SOLUTION FOR RAPID CONTROL PROTOTYPING IN WINDOWS ®.QUARC generates real-time code directly from Simulink®-designed controllers and runs the generated code in real-time on the Windows® target - all on the same PC. The Data Acquisition Card seamlessly interfaces with Simulink® using Hardware-in-the-loop blocks provided in the QUARC T argets Library.SPLIT SECOND CONTROL DESIGN – A DECADE IN ThE MAkINGQUARC was built on the legacy of WinCon, the first real-time software to run Simulink®-generated code in Windows®. QUARC seamlessly integrates with Simulink® and redefines the traditional design-to-implementation interface toolset. Just click a button to enjoy more functionality and development flexibility, all geared towards improved real-time performance. Academics havesuccessfully deployed many advanced control and mechatronic systems, ranging from intelligent unmanned systems to force-feedback-enabled virtual reality.ADVANCEDINDUSTRIAL R&DACADEMIA INDUSTRYFOUR USES OF QUARCCONTROLS EDUCATION INNOVATIVERESEARCH GRADUATE-LEVEL EXPLORATION Enhance your engineering courses with industry- relevant hands-on learning Explore practical solutions for real-life challenges with a synergistic approachConduct ground-breaking research in emerging areas such as Unmanned Vehicle Systems and hapticsFast track time-to-market with an affordable rapid control prototyping solutionChoosing software for control system design andimplementation is critical for timely, successful research and development. Quanser knows this because we’ve pioneered control engineering for over 20 years. That’s why we created QUARC – a powerful rapid control prototyping tool that significantly accelerates control design and implementation. initially designed for industrial demands, QUARC is nonetheless ideal foradvanced research, masters-level, and evenundergraduate, teaching. QUARC is an integral part of all Quanser control lab workstations and is used all over the world by thousands of educational institutions and organizations, including the Canadian Space Agency and Defense Research and Development Canada. Discover what QUARC can help you achieve in less time and effort than you might be spending now.ACCELERATE CONTROLS EDUCATIONQUARC is an ideal tool to teach control concepts. It allows students to draw a controller, generate code and run it - all without Digital Signal Processing or without writing a single line of code. The capabilities of this powerful yet adaptable software are emphasized by the comprehensive curriculum that accompanies Quanser’s control lab equipment. The supplied Instructor and Student Workbooks feature lab exercises and projects based on Simulink®. They help focus students’ efforts on key control concepts rather than tedious code writing. The curriculum is developed by engineers for engineers to effectively demonstrate and teach the mechatronic design approach practised in industry. This includes modeling, controller design, simulation and implementation. An excellent low-cost rapid control prototyping system, QUARC is being usedby thousands of institutions worldwide. It is an effective and efficient teaching tool for undergraduate and graduate-level courses in classical and modern control theory.hOW QUARC FUSES MULTIPLEENGINEERING COURSESThe Integrated Learning Centre at Queen’s University fuses all engineering disciplines into one modern lab. Quanser’s workstations, featuring a wide range of modular Quanser experiments, are used here to teach introductory, intermediate and advanced controls. QUARC software is an integral part of all those workstations. An economical approach to outfitting a lab, it also keeps students motivated, providing access to even more hands-on learning.CONTROLS EDUCATIONis done, allowing the studentsto focus more on the controldesign theory and less on theworkings of MATLABSimulink, thus improvingthe learning experience.”Dr. Wen-Hua Chen,Loughborough University,United KingdomThis Flexible Link module furtherexpands your topics of study withthe SRV02 workstation.All on a Single PCQUARC provides a single PC solution for rapid control prototypingin Windows XP® or Vista®. It generates real-time code directly fromSimulink®-designed controllers – but for the same PC. This single PCSolution for rapid control prototyping significantly accelerates controldesign and implementation. This helps students focus on theimportant aspects of the control design process and completeproject-based assignments successfully.Simple. Intuitive.QUARC user interfaces are easy to understand without training.For example, QUARC’s “external mode” communications allow theSimulink® diagram to communicate with real-time code generatedfrom the model. Tune parameters of the running model by changingblock parameters in the Simulink® diagram. Want to view the statusof a signal in the model? Simply open a Simulink® Scope (or any otherSink in the diagram) while the model runs on the target. Furthermore,data can be streamed to the MATLAB® workspace or to a file on diskfor off-line analysis.Low MaintenanceQUARC streamlines the process of maintaining and servicing a laboratorywithout sacrificing system performance or an excessive amount of yourstaff’s time. The extremely flexible host-target structure allows QUARC usersto maximize limited resources (i.e. PC, laptop and hardware) with minimaleffort or cost. Host (control design environment) and target (platformwhich executes the real-time code) can be on separate computers yet stillcommunicate through a network connection. QUARC can sustain anypossible multi-configuration. Ask about License Server Architecture.The Integrated Learning Center, Queen’s University, Canada.BRING ThEORIES TO LIFEWhether you’re exploring emerging technologies or transforming knowledge into solutions for real-world challenges, count on Quanser to help you achieve your research goals. The power of QUARC software combined with Quanser’s innovative plants can helpresearchers test their theories in real-time, on real hardware. QUARC seamlessly integrates with Quanser’s research platforms toimplement virtually any control algorithm. Combine QUARC with Quanser’s multi-function Data Acquisition card and plants to create a self-contained control workstation ideal for advanced research. Use it to design, simulate, implement, and test a variety of time-varyingsystems: communications, controls, signal processing, video processing, and image processing.All this is achievable quickly , easily and affordably because the workstation is a fully integrated, open-architecture solution.The set-up pictured below shows a 3 DOF Gyroscope workstation as one example of a Quanser workstation for high level research. This typical configuration entails: • P lant • Amplifier• Data Acquisition Card • Virtual Plant Simulation• Rapid Control Prototyping Design Software • Pre-designed ControllersFor more information about the Quanser’s research platformsplease visit /MCC.14323 DOF GYROSCOPEFeaturing three Degrees Of Freedom (DOF), this dynamically diverse experimental platform is ideal for teaching rotational dynamic challenges.DATA ACQUISITION CARDMeasure and command real-time signals with high I/Osampling period. QUARC supports a wide range of Quanser and National Instruments data acquisition cards. For a complete list please visit /QUARC.AMPLIFIER AMPAQQuanser’s multi-channel linear current amplifier is ideal forprecision controls. The AMPAQ connects to the DAQ terminal board and is connected to the 3-DOF Gyroscope with its easy-connect cables.SOFTWARE TO ACCELERATE DESIGN3-DOF Gyroscope models are designed to run in real-time with QUARC ® software, which integrates seamlessly withMATLAB ®/Simulink ®.“Using Quanser’s software, we can easily design control systems for many plants. We can apply complex control strategies quickly and effectively - and it is very easy to verify theory on the real plant.”Kenichi yano,Associate Professor, Gifu University , JapanEFFORTLESS INTEGRATION FOR MEChATRONIC RESEARChQUARC is a powerful, flexible mechatronic integration tool, providing time-saving and simple solutions to those unique challenges encountered when you’re developing mechatronic systems. Whether you have custom-made research platforms or use manufactured equipment, QUARC is the only software that makes it easy to interface with all of them. QUARC offers a suite of third-party device blocks which help researchers seamlessly interface and control KUKA robots, PGR cameras and SensAble® PHANTOM devices, to name a few. These blocks not only allow a Simulink® model to communicate with external devices but also implement the mathematical framework for controlling them. All this is possible without the need to learn new tools or hand coding since the controller design and integration is performed in an environment most researchers are familiar with, such as Windows®, MATLAB®, Simulink®.“QUARC’s support of TCP/IP has been a tremendous help for our research. It allowed us to develop a distributed sensing system that isn’t dependent on expensive I/O hardware or DAQ boards. Further, this allows for safety-critical redundancy when we aredoing vehicle control tests.”Sean Brennan,Department of Mechanical and Nuclear Engineering,Pennsylvania State University , USAQUARC OFFERS OVER 10 BLOCKSETSThe table provides an overview. At a glance,you can see specific research applications, unique attributes and technical specifications.Now you can enjoy greater flexibility whenimplementing control schemes. QUARC expands the possibilities for complex control design by:multiple operating Systems Support.QUARC is designed so that code could be generated for multipleoperating systems and hardware platforms while maintaining a common, seamless and easy-to-use interface. Simulink® models can run in real-time on a variety of targets - a target being acombination of operating system and processor for which QUARC generates code from a Simulink® diagram. Targets includeWindows® and QNX®. The number of targets QUARC supports is continually increasing.Support for Communications.The QUARC Stream API offers a flexible and protocol-independent communications framework. Conduct standard communication between QUARC models and more: between a QUARC model and an external third-party application (e.g., graphical userinterface) or even between two external third-party applications. The Stream API is independent of the development environment and can be used in C/C++, .NET, MATLAB®, LabVIEW TM , etc. The Stream API enables the communication between multiple real-time model over the internet. This could be used for distributed control, teleoperation, device interfacing, etc. The stream API natively supports the following protocols: TCP/IP, UDP, serial, shared memory , named pipes, ARCNET, and more.For demos and tutorials on QUARC’s communication capabilities request a free trial of QUARC at /QUARC.increasing number of Blocksets.The number of interfaces QUARC supports is continuallyincreasing over time to ensure easy integration with recent and popular third-party devices. Here are a few more examples: • Nintendo Wiimote• Q bot- An Unmanned Ground Vehicle based on iRobot Create®• Schunk Grippers• SparkFun Electronics SerAccelGet an updated list of interfaces supported by QUARC at /QUARC/blocksetsDESCRIPTIONUsing the KUKA Robot Blockset you can control any KUKA robot equipped with RSI (Robot SensorInterface) through the interactive Simulink® environment without tedious hand coding and cumbersome hardware interfacing.This blockset is not included in the standard QUARC license and is sold separately.The Point Grey Research (PGR) Blockset is used to acquire images from some of the Point Grey Research cameras. QUARC also provides image processing blocksets that can be used to find objects of a given color within a source image or convert images from one format to another.This blockset is included in the standard QUARC license.The Wiimote (Wii Remote) block reads the state of the Wiimote and outputs the button, acceleration, and Infra Red (IR) camera information. Using this blockset you can easily interface the Wiimote into the controller. This blockset is included in the standard QUARC license.The Novint Falcon Blockset is used for implementing control algorithms for the Falcon haptic device. Using the Blockset significantly simplifies the task of designing controllers for the Falcon.This blockset is included in the standard Quarc license.TEChNICAL CAPABILITIES AND SPECIFICATIONS• E nables the deployment of real-time executables with GUI • S upport for setting and getting values (e.g., knobs, displays, scopes, and other inputs and outputs)Supported devices:• SensAble PHANTOM Omni • SensAble PHANTOM Desktop • SensAble PHANTOM Premium• SensAble PHANTOM Premium 6DOF Data provided as output,• GPS position (latitude, longitude, altitude)• Number of visible satellites (dilution of precision data)• Accuracy information (dilution of precision – DOP)Typical accuracy 1-3m (WAAS)SUGGESTED RESEARCh APPLICATIONS• GUI Design (e.g. Cockpit)• Force feedback virtual reality• Haptically-enabled medical simulations • Teleoperation• Precise robotic manipulation• Image-based control and localization • Autonomous navigation and control • Fault detection• Image-based control and localization• Autonomous navigation and control • Image recognition • Mapping• Obstacle detection and avoidance • Visual servoing and tracking • Vision feedback• Teleoperation• Robotic manipulation• Force feedback virtual reality• Haptically enabled medical simulations • Teleoperation• Localization• Autonomous navigation and control• M ission reconfiguration(e.g., for Unmanned Vehicle Systems)• Fault recovery • Safety watchdogDYNAMICRECONFIGURATIONkUkA ROBOT ALTIASENSABLEPhANTOM ® SERIESVISUALIzATIONPGR CAMERASWII REMOTENOVINT FALCONGPSNATURAL POINTOPTITRACkThe PHANTOM® Blockset lets you control the series of PHANTOM® haptic devices via Simulink®. For added flexibility researchers can combine the Phantom Blockset and Visualization Blockset to enjoy seamless haptics rendering of virtual environments.This blockset is not included in the standard QUARC license and is sold separately.The Visualization Blockset creates 3D visualizations of simulations or actual hardware in real-time. By combining meshes and textures, you can create objects to seamlessly integrate high-performance graphics with real-time controllers. Comprehensive documentation and examples along with additional content are provided to help new users get started and master this blockset quickly. QUARC Visualization blockset is used in the Virtual Plant Simulation of selected Quanser plants such as SRVO2 and Active Suspension. This blockset is included in the standard QUARC license.• Y coordinates of up to four IR points detected by the wiimote IR camera. Valid values range from 0 to 767 inclusive.• A compatible Bluetooth device must be installed on the PC• A bility to command either Cartesian or joint velocity set points • A bility to measure the Cartesian positions, joint angles and joint torques • A bility to set either Cartesian or the joint minimum and maximum velocity limits • K UKA built-in safety checks are still enabled for safe operation• S end forces and torques in Cartesian or joint space • Read encoder values, position, and joint angles• Send commands in two different work spaces to the Phantom device • T he block outputs the gimbal angles of the device plus the values associated with the buttons and the 7 DOF available on the device (thumb-pad or scissors)• R emotely connect to a visualization server with multiple clients • N o interference with the operation of your real-time controller• Plugins provided for Blender and Autodesk’s 3ds Max 2008, 2009 and 2010• S et different material properties such as diffuse color, opacity , specular color, shininess, and emissivity.• T exture map support for png, jpg, tiff, and bmp.• X 3D support• C onfigurable mouse and keyboard interface for manually navigating around the environment • P erformance far exceeds TMW’s Virtual Reality toolbox• U p to 16 cameras can be connected and configured for single or multiple capture volumes • C apture areass up to 400 square feet • S ingle point tracking for up to 80 markers, or 10 rigid-body objects • T ypical calibration time is under 5 minutes • P osition accuracy on the order of mm under typical conditions• U SB 2.0 connectivity to ground station PC• U p to 100 fps tracking• S upport for Draganflyer 2 HI-COL and the FireflyMV • F rame rate selection from 7.5 fps to 60 fps • R esolutions from 640 x 480 to 1024 x 768, • C olor or grayscale, and custom image (subimage) sizes supported for faster framerates• C ontinuity of states between the model being switched-out and the model being switched-in, as a necessary condition to the system stability • S witching within one sampling interval, as a necessary condition to the system stability • D ynamic reconfiguration can be triggered either automatically (e.g., from a supervisory model) or manually• D ynamic Reconfiguration can be triggered either locally or remotely (i.e., on a remote target)The OptiTrack Blockset allows motion capture and tracking by using 3 or more synchronized infrared (IR) cameras that capture images containing reflective markers within a workspace. The blockset can be used to track either individual markers or rigid bodies. This Blockset makes it easy to conduct vision-based control experiments in real-time, especially for objects that were previously difficult to track, such as indoor autonomous vehicles.This blockset is not included in the standard QUARC license and is sold separately.The GPS Blockset allows GPS receivers to be easily accessed, thereby adding GPS localization to an experimentalplatform. This Blockset integrates with Ublox GPS devices as well as NMEA compliant GPS devices. This blockset is not included in the standard Quarc license and is sold separately.The Altia Design Blockset enables the user to interact with the real-time code from Altia GUIs. Unlike theMATLAB® GUIs, MATLAB® and Simulink® are not required when using Altia GUIs. This blockset gives you the tools you need to generate complete production systems without writing a single line of code. This blockset is included in the standard QUARC license.The Dynamic Reconfiguration Blockset lets you dynamically switch models on the target machine within a sampling interval. A running model may be replaced with another model while ensuring continuity of states between both with no interruptions (i.e. no skipped sample). For a demo and tutorial on the Dynamic Reconfiguration blockset request a free trial of QUARC at /QUARC.This blockset is not included in the standard QUARC license and is sold separately.Data provided as output:• P osition: X, Y, and Z position in Cartesian coordinates• Button information: Whether a button is currently pressed or not • F orce: X, Y, and Z forces applied by the Falcon end-effectormodel 1model 2* Please note that prices for blocksets may vary. For more information or to request a quote please contact sales@.• Payload 5 kg • Number of axes 6• Repeatability <±0.02 mm • Weight 28 kg• Mounting positions floor or ceiling • Controller KR C2sr • Max speed 8.2 m/sData provided as output:• X, Y, and Z axis accelerations • Button states • X coordinates of up to four IR points detected by the wiimote IR camera. Valid values range from 0 to 1023 inclusive• S upport for setting values (i.e. Meters and other outputs)• F eatures the Quanser Plot library for AltiaBLOCkSET* • Virtual reality rendering• Game and medical simulation• Simulation of mechanical components • Data fusion • R eal-time status displays of physical hardware• Virtual cockpit for aerial vehicles REQUEST A FREE 30 DAY TRIAL OF QUARC TODAY. VISIT /QUARC• Robotic manipulation • Teleoperation“The Host Computer System for the Challenging Environment Assessment Laboratory (CEAL) at the Toronto Rehabilitation Institute (TRI) was developed using Quanser’s QU ARC real-time software. The power of QU ARC, with Quanser’s engineering support, enabled TRI to create a flexible developmentenvironment for researchers to implement sophisticated real-time experiments, using a large-scale 11-ton, 6-DOF motion platform and high-performance audio-visual rendering systems”Dr. Geoff Fernie , Vice President, Toronto Rehabilitation Institute, CanadaQUARC ACCELERATES MEChATRONIC DEVELOPMENT WITh RAPID CONTROL PROTOTYPINGQUARC is a powerful Rapid Control Prototyping (RCP) platform that meets industrial research and development demands. This robust software helps manage the increasing complexity of controlengineers’ tasks and accelerates their ability to test control strategies. Generating countless iterations of Simulink® control designsbecomes almost effortless - a block diagram design is automatically implemented on the system and computed in real time, eliminating the need for manual coding. This RCP platform is adaptable to virtually any mechatronic interfaces and scalable for complex multi-input and multi-output systems.Affordable Industrial-Grade PerformanceFor a fraction of the cost of comparable systems, Research and Development engineers can convert a PC into a powerful platform for control system development and deployment. When combined with a Quanser Power Amplifier and a Quanser Data Acquisition Card, QUARC software provides an ideal rapid prototyping and hardware-in-the-loop development environment. QUARC is also compatible with a wide range of commercially available data acquisition cards, including National Instruments boards.QUARC evolved from experience with its predecessor WinCon.The Canadian Space Agency played an intricate role in defining and confirming many of the features of QUARC. This was done in the context of their micro-satellite development program on an early stage prototype. It has since been adopted by industries requiring the latest in performance and development flexibility such as the Aerospace, Defence and Medical device industries.QUARC capabilities and features are designed to optimize the RCP process. Below are a few samples of such features.• F lexible and extensible communications blocks configurablefor real-time TCP/IP, UDP, serial, shared memory and other protocols • P erformance Diagnostics • R TW Code Optimization support • M odularity and incremental builds via model referencing • C ontrol of thread priorities and CPU affinity • A synchronous execution (e.g., ideal for efficient communication) • R un any number of models on one target – or simultaneously on multiple targets • S elf-booting models for embedded targets• E xternal Hardware-In-the-Loop card and communication interfacing provided in C/C++, MATLAB®, LabVIEW TM , and .NET languages • M ultiprocessor (SMP) support, e.g., on a quad-core Windows target QUARC models can take advantage of all four cores. • S imulink® 3D Animation (formerly known as Virtual Reality) Toolbox support• A bility to interface with MATLAB® GUIs, LabVIEW TM panels, and Altia“We have been using Quanser’s QU ARC software to do real-time robot control. QU ARC enables fast and easy prototyping of control algorithms with hardware in the loop and has been an invaluable tool for algorithm development, simulation, and verification.”Paul Bosscher, Harris Corporation, USAChallenging environment AssessmentLaboratory (CeAL) will be one of the most advanced rehabilitation research facilities in the world.INNO VATE, RESEARCHAND EXPLOIT KNOWLEDGE.QU ANSERCONSULTING SOFTWAREHARDWAREPlantDAQAmplifierQUARC®: A POWERFUL ENGINEFOR ENGINEERING DEPARTMENTSThree issues challenge university engineering departments everywhere: teaching, research and budget. One solution resolves them: QUARC software from Quanser!For T eaching: Created by engineers for engineers, QUARC is an excellent low-cost rapid control prototyping system. Working seamlessly with Simulink®, QUARC helps students put ideas andtheory into practice sooner. Plus curriculum is offered to help educators focus on what matters most. With more hands-on learning, undergraduate and graduate students alike are captivated and motivated to study further.For Research: Originally designed for industrial use, QUARC is idealfor advanced research. From the precise control of surgical robots to unmanned air vehicles and beyond, ideas can be tested in real-time- even ideas that are out of this world. Small wonder our client list includes NASA, the Canadian Space Agency and thousands of universities and colleges. (Look on your left.)For your department’s budget: QUARC seamlessly integrates over80 Quanser experiments - from introductory to very advanced. These are modular by design and maximize efficiencies, offering multiple uses for one workstation. Academics ourselves, Quanser appreciates your need for careful budgeting. So QUARC is competitively pricedand available with single- or multiple-user licenses.Learn more at /QUARCProducts and/or services pictured and referred to herein and their accompanying specifications may be subject to change without notice. Products and/or services mentioned herein are trademarks or registered trademarks of Quanser Inc. and/or its affiliates. Other product and company names mentioned herein are trademarks or registered trademarks of their respective owners.©2010 Quanser Inc. All rights reserved. Rev 2.0。
Average,期望值,ab initio, 从头计算approximate,近似accurate, 精确atomiticity, 粒子性active, 活性的adiabatic, 绝热的,非常缓慢的anti-symmetry principle 反对称原理Basis,基组bra, 左矢,左矢空间,右矢空间的对偶空间boundary,边界条件Born-Oppenheimer 波恩奥本海默近似,绝热近似退耦后的进一步近似Configuration, 组态,电子排布correlation, 电子的相关作用commutation, 对易子coordinate, 坐标conjugate, 共轭core, 原子实convergence, 收敛,级数或积分收敛coupling, 耦合Coulomb’s Law, 库仑定律,麦克斯韦场方程的点电荷近似correspondence principle, 对应原理complete, 完备的complete active space (CAS), 完备的活性空间closed-shell, 闭壳层closed system, 封闭体系configuration state function (CSF)组态波函数Diagonalization,对角化Diagonal, 对角阵,对角元DFT, 密度泛函理论density,电子密度D-CI, double CIdynamical, 动力学的deterministic, 行列式的diabatic 未对角化的,非自身表象的,透热的Effective Hamiltonian, 有效哈密顿electron, 电子eigenvalue, 本征值eigenvector, 本征矢,无限维Hilbert空间中的态矢量external, 外加的energy, 能量excitation, 激发态excited, 被激发的exclusion principle不相容原理Functional, 泛函数function, 函数Fock space, Fock空间force, 力.,field场Gradient,梯度Gaussian, 高斯程序,高斯函数generic, 普适的Gauge 规范Hamiltonian, 哈密顿,Hessian, 二阶导数Hermitian, 厄米的Hartree 原子能量单位Integral, 积分internal, 内部的(内部自由度的)interaction, 相互作用independent, 不独立的invariant, 不变的iteration, 叠代interpretation, (几率)诠释interpolation,inactive不活动的J-integral, j积分jj-coupling jj耦合K-integral, k积分ket,右矢,右矢空间Linear algebra, 线性代数,linear combination of atomic orbitals (LCAO),原子轨函线性组合(法)local, 定域的locality, 定域物理量linear scaling, 线性标度low order,低对称性,有序度较低的情形Matrix, 矩阵,metric,矩阵的momentum, momenta,动量many-body theory,多体理论mechanics,力学,机理,机制multiconfiguration self-consistent field (MCSCF),多组态自洽场multireference (MR),多参考态方法minimization,最小化Normalization,归一化normal order, 正常序norm,已归一化的(波函数),N-electron, N电子体系nondynamic,非动力学的nonadiabtaic 非绝热的,有交换作用的,非渐变的Orbit,轨道orbital,轨道波函数,轨函observable, 可观测的(物理量)operator, 算符optimization, 优化one-electron,单电子,orthogonal, 正交的orthonormal, 正交归一的,open-shell,开壳层open system,开放体系,order-N第N阶(近似,导数)Principle,原理,原则property,性质particle, 粒子probability, 几率probabilistic, 几率性的potential,势PES, 势能面pseudo-, 赝的,pseudo vector赝矢量,pseudopotential,赝势perturbation theory,微扰理论Quantum, quanta, 量子quantized, 使量子化quantization,量子化的过程quotient,商quantity,数量,物理量Relativity,相对论,relativistic, 相对论性的representation,表示,表象Reference,参考系,参考态Spin, 自旋S-matrix, s矩阵,线性变换矩阵,散射矩阵symmetry, 对称性SCF, 自洽场stability,稳定性state,态scale,标度,测量shell,电子壳层spin-orbit coupling,自旋轨道耦合static,静态的space,空间,坐标空间的,banach/Hilbert Space,巴拉赫,希尔伯特空间spatial,空间的similarity transformation, 相似变换self-consistent field (SCF), 自洽场secondary ,二阶的,二级的,second quantization,二次量子化Transition state,过渡态time-dependent,含时的,对时间依赖的trace,矩阵的迹.Transformation,变换Universal,统一的,全同的。
高中英语世界著名科学家单选题50题1. Albert Einstein was born in ____.A. the United StatesB. GermanyC. FranceD. England答案:B。
解析:Albert Einstein(阿尔伯特·爱因斯坦)出生于德国。
本题主要考查对著名科学家爱因斯坦国籍相关的词汇知识。
在这几个选项中,the United States是美国,France是法国,England是英国,而爱因斯坦出生于德国,所以选B。
2. Isaac Newton is famous for his discovery of ____.A. electricityB. gravityC. radioactivityD. relativity答案:B。
解析:Isaac Newton 艾萨克·牛顿)以发现万有引力gravity)而闻名。
electricity是电,radioactivity是放射性,relativity 是相对论,这些都不是牛顿的主要发现,所以根据对牛顿主要成就的了解,选择B。
3. Marie Curie was the first woman to win ____ Nobel Prizes.A. oneB. twoC. threeD. four答案:B。
解析:Marie Curie 居里夫人)是第一位获得两项诺贝尔奖的女性。
这题主要考查数字相关的词汇以及对居里夫人成就的了解,她在放射性研究等方面的贡献使她两次获得诺贝尔奖,所以选B。
4. Thomas Edison is well - known for his invention of ____.A. the telephoneB. the light bulbC. the steam engineD. the computer答案:B。
解析:Thomas Edison( 托马斯·爱迪生)以发明电灯(the light bulb)而闻名。
量⼦⼒学简史--超详细的发展介绍量⼦⼒学的创⽴是⼀段充满传奇英雄和故事的令⼈⼼潮澎湃的历史,其中的每个⼈物都值得我们每代⼈去颂扬,每个突破都值得我们去细细回味。
让我们记住这些英雄的名字:普朗克、爱因斯坦、玻尔、德·布罗意、海森堡、泡利、狄拉克、费⽶、玻恩、玻⾊、薛定谔......他们中的每个⼈及其取得的成就都值得我们⽤书、⾳乐、电影、互联⽹等所有可能的传媒来记录、传播。
他们和他们的科学超越国界,属于我们整个⼈类。
由于篇幅的限制,笔者在这⾥只能做简短的介绍。
1、量⼦的诞⽣普朗克(Max Planck, 1858-1947 ) 从任何⾓度看都是⼀个典型的知识分⼦。
他1858年出⽣于⼀个知识分⼦家庭,曾祖⽗和祖⽗都是神学教授,⽗亲则是法学教授。
他从⼩受到了优良的教育,他会包括钢琴、管风琴和⼤提琴在内的多种乐器,会作曲和写歌,但他最终选择了物理。
普朗克事业⾮常顺利,21岁获得博⼠学位,随后开始在研究上取得进展,27岁成为基尔( Kiel )⼤学的副教授,31岁继任基尔克夫( Gustav Robert Kirchhoff, 1824-1887)在柏林⼤学的位置,3年后成为柏林⼤学的正教授。
他为⼈正直、诚实,没有任何怪癖和奇闻异事。
如果没有发现“量⼦”,他可能也会和其他典型的知识分⼦、名牌⼤学教授⼀样埋没在历史的尘埃⾥。
1894年普朗克做了个改变整个物理史的决定,他开始研究⿊体辐射。
⿊体是⼀种能够吸收所有⼊射光的物体,远处建筑物上⿊洞洞的窗户就是⿊体。
⿊体在吸收所有⼊射光的同时也会向外辐射光。
最早研究⿊体辐射的正是普朗克的前任基尔克夫。
前期的研究表明⿊体辐射和构成⿊体的具体材料⽆关,是普适的。
后来维恩(Wilhelm Wien, 1864-1928 )发现了⼀个公式,表明⿊体的辐射功率和辐射频率之间有⼀个普适的关系。
从1894年开始,在接下来的五年左右时间⾥,普朗克在⿊体辐射⽅⾯发表了⼀系列⽂章,但没有实质性的突破。
华中师范大学物理学院物理学专业英语仅供内部学习参考!2014一、课程的任务和教学目的通过学习《物理学专业英语》,学生将掌握物理学领域使用频率较高的专业词汇和表达方法,进而具备基本的阅读理解物理学专业文献的能力。
通过分析《物理学专业英语》课程教材中的范文,学生还将从英语角度理解物理学中个学科的研究内容和主要思想,提高学生的专业英语能力和了解物理学研究前沿的能力。
培养专业英语阅读能力,了解科技英语的特点,提高专业外语的阅读质量和阅读速度;掌握一定量的本专业英文词汇,基本达到能够独立完成一般性本专业外文资料的阅读;达到一定的笔译水平。
要求译文通顺、准确和专业化。
要求译文通顺、准确和专业化。
二、课程内容课程内容包括以下章节:物理学、经典力学、热力学、电磁学、光学、原子物理、统计力学、量子力学和狭义相对论三、基本要求1.充分利用课内时间保证充足的阅读量(约1200~1500词/学时),要求正确理解原文。
2.泛读适量课外相关英文读物,要求基本理解原文主要内容。
3.掌握基本专业词汇(不少于200词)。
4.应具有流利阅读、翻译及赏析专业英语文献,并能简单地进行写作的能力。
四、参考书目录1 Physics 物理学 (1)Introduction to physics (1)Classical and modern physics (2)Research fields (4)V ocabulary (7)2 Classical mechanics 经典力学 (10)Introduction (10)Description of classical mechanics (10)Momentum and collisions (14)Angular momentum (15)V ocabulary (16)3 Thermodynamics 热力学 (18)Introduction (18)Laws of thermodynamics (21)System models (22)Thermodynamic processes (27)Scope of thermodynamics (29)V ocabulary (30)4 Electromagnetism 电磁学 (33)Introduction (33)Electrostatics (33)Magnetostatics (35)Electromagnetic induction (40)V ocabulary (43)5 Optics 光学 (45)Introduction (45)Geometrical optics (45)Physical optics (47)Polarization (50)V ocabulary (51)6 Atomic physics 原子物理 (52)Introduction (52)Electronic configuration (52)Excitation and ionization (56)V ocabulary (59)7 Statistical mechanics 统计力学 (60)Overview (60)Fundamentals (60)Statistical ensembles (63)V ocabulary (65)8 Quantum mechanics 量子力学 (67)Introduction (67)Mathematical formulations (68)Quantization (71)Wave-particle duality (72)Quantum entanglement (75)V ocabulary (77)9 Special relativity 狭义相对论 (79)Introduction (79)Relativity of simultaneity (80)Lorentz transformations (80)Time dilation and length contraction (81)Mass-energy equivalence (82)Relativistic energy-momentum relation (86)V ocabulary (89)正文标记说明:蓝色Arial字体(例如energy):已知的专业词汇蓝色Arial字体加下划线(例如electromagnetism):新学的专业词汇黑色Times New Roman字体加下划线(例如postulate):新学的普通词汇1 Physics 物理学1 Physics 物理学Introduction to physicsPhysics is a part of natural philosophy and a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the Scientific Revolution in the 17th century, the natural sciences emerged as unique research programs in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry,and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences, while opening new avenues of research in areas such as mathematics and philosophy.Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products which have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.Core theoriesThough physics deals with a wide variety of systems, certain theories are used by all physicists. Each of these theories were experimentally tested numerous times and found correct as an approximation of nature (within a certain domain of validity).For instance, the theory of classical mechanics accurately describes the motion of objects, provided they are much larger than atoms and moving at much less than the speed of light. These theories continue to be areas of active research, and a remarkable aspect of classical mechanics known as chaos was discovered in the 20th century, three centuries after the original formulation of classical mechanics by Isaac Newton (1642–1727) 【艾萨克·牛顿】.University PhysicsThese central theories are important tools for research into more specialized topics, and any physicist, regardless of his or her specialization, is expected to be literate in them. These include classical mechanics, quantum mechanics, thermodynamics and statistical mechanics, electromagnetism, and special relativity.Classical and modern physicsClassical mechanicsClassical physics includes the traditional branches and topics that were recognized and well-developed before the beginning of the 20th century—classical mechanics, acoustics, optics, thermodynamics, and electromagnetism.Classical mechanics is concerned with bodies acted on by forces and bodies in motion and may be divided into statics (study of the forces on a body or bodies at rest), kinematics (study of motion without regard to its causes), and dynamics (study of motion and the forces that affect it); mechanics may also be divided into solid mechanics and fluid mechanics (known together as continuum mechanics), the latter including such branches as hydrostatics, hydrodynamics, aerodynamics, and pneumatics.Acoustics is the study of how sound is produced, controlled, transmitted and received. Important modern branches of acoustics include ultrasonics, the study of sound waves of very high frequency beyond the range of human hearing; bioacoustics the physics of animal calls and hearing, and electroacoustics, the manipulation of audible sound waves using electronics.Optics, the study of light, is concerned not only with visible light but also with infrared and ultraviolet radiation, which exhibit all of the phenomena of visible light except visibility, e.g., reflection, refraction, interference, diffraction, dispersion, and polarization of light.Heat is a form of energy, the internal energy possessed by the particles of which a substance is composed; thermodynamics deals with the relationships between heat and other forms of energy.Electricity and magnetism have been studied as a single branch of physics since the intimate connection between them was discovered in the early 19th century; an electric current gives rise to a magnetic field and a changing magnetic field induces an electric current. Electrostatics deals with electric charges at rest, electrodynamics with moving charges, and magnetostatics with magnetic poles at rest.Modern PhysicsClassical physics is generally concerned with matter and energy on the normal scale of1 Physics 物理学observation, while much of modern physics is concerned with the behavior of matter and energy under extreme conditions or on the very large or very small scale.For example, atomic and nuclear physics studies matter on the smallest scale at which chemical elements can be identified.The physics of elementary particles is on an even smaller scale, as it is concerned with the most basic units of matter; this branch of physics is also known as high-energy physics because of the extremely high energies necessary to produce many types of particles in large particle accelerators. On this scale, ordinary, commonsense notions of space, time, matter, and energy are no longer valid.The two chief theories of modern physics present a different picture of the concepts of space, time, and matter from that presented by classical physics.Quantum theory is concerned with the discrete, rather than continuous, nature of many phenomena at the atomic and subatomic level, and with the complementary aspects of particles and waves in the description of such phenomena.The theory of relativity is concerned with the description of phenomena that take place in a frame of reference that is in motion with respect to an observer; the special theory of relativity is concerned with relative uniform motion in a straight line and the general theory of relativity with accelerated motion and its connection with gravitation.Both quantum theory and the theory of relativity find applications in all areas of modern physics.Difference between classical and modern physicsWhile physics aims to discover universal laws, its theories lie in explicit domains of applicability. Loosely speaking, the laws of classical physics accurately describe systems whose important length scales are greater than the atomic scale and whose motions are much slower than the speed of light. Outside of this domain, observations do not match their predictions.Albert Einstein【阿尔伯特·爱因斯坦】contributed the framework of special relativity, which replaced notions of absolute time and space with space-time and allowed an accurate description of systems whose components have speeds approaching the speed of light.Max Planck【普朗克】, Erwin Schrödinger【薛定谔】, and others introduced quantum mechanics, a probabilistic notion of particles and interactions that allowed an accurate description of atomic and subatomic scales.Later, quantum field theory unified quantum mechanics and special relativity.General relativity allowed for a dynamical, curved space-time, with which highly massiveUniversity Physicssystems and the large-scale structure of the universe can be well-described. General relativity has not yet been unified with the other fundamental descriptions; several candidate theories of quantum gravity are being developed.Research fieldsContemporary research in physics can be broadly divided into condensed matter physics; atomic, molecular, and optical physics; particle physics; astrophysics; geophysics and biophysics. Some physics departments also support research in Physics education.Since the 20th century, the individual fields of physics have become increasingly specialized, and today most physicists work in a single field for their entire careers. "Universalists" such as Albert Einstein (1879–1955) and Lev Landau (1908–1968)【列夫·朗道】, who worked in multiple fields of physics, are now very rare.Condensed matter physicsCondensed matter physics is the field of physics that deals with the macroscopic physical properties of matter. In particular, it is concerned with the "condensed" phases that appear whenever the number of particles in a system is extremely large and the interactions between them are strong.The most familiar examples of condensed phases are solids and liquids, which arise from the bonding by way of the electromagnetic force between atoms. More exotic condensed phases include the super-fluid and the Bose–Einstein condensate found in certain atomic systems at very low temperature, the superconducting phase exhibited by conduction electrons in certain materials,and the ferromagnetic and antiferromagnetic phases of spins on atomic lattices.Condensed matter physics is by far the largest field of contemporary physics.Historically, condensed matter physics grew out of solid-state physics, which is now considered one of its main subfields. The term condensed matter physics was apparently coined by Philip Anderson when he renamed his research group—previously solid-state theory—in 1967. In 1978, the Division of Solid State Physics of the American Physical Society was renamed as the Division of Condensed Matter Physics.Condensed matter physics has a large overlap with chemistry, materials science, nanotechnology and engineering.Atomic, molecular and optical physicsAtomic, molecular, and optical physics (AMO) is the study of matter–matter and light–matter interactions on the scale of single atoms and molecules.1 Physics 物理学The three areas are grouped together because of their interrelationships, the similarity of methods used, and the commonality of the energy scales that are relevant. All three areas include both classical, semi-classical and quantum treatments; they can treat their subject from a microscopic view (in contrast to a macroscopic view).Atomic physics studies the electron shells of atoms. Current research focuses on activities in quantum control, cooling and trapping of atoms and ions, low-temperature collision dynamics and the effects of electron correlation on structure and dynamics. Atomic physics is influenced by the nucleus (see, e.g., hyperfine splitting), but intra-nuclear phenomena such as fission and fusion are considered part of high-energy physics.Molecular physics focuses on multi-atomic structures and their internal and external interactions with matter and light.Optical physics is distinct from optics in that it tends to focus not on the control of classical light fields by macroscopic objects, but on the fundamental properties of optical fields and their interactions with matter in the microscopic realm.High-energy physics (particle physics) and nuclear physicsParticle physics is the study of the elementary constituents of matter and energy, and the interactions between them.In addition, particle physicists design and develop the high energy accelerators,detectors, and computer programs necessary for this research. The field is also called "high-energy physics" because many elementary particles do not occur naturally, but are created only during high-energy collisions of other particles.Currently, the interactions of elementary particles and fields are described by the Standard Model.●The model accounts for the 12 known particles of matter (quarks and leptons) thatinteract via the strong, weak, and electromagnetic fundamental forces.●Dynamics are described in terms of matter particles exchanging gauge bosons (gluons,W and Z bosons, and photons, respectively).●The Standard Model also predicts a particle known as the Higgs boson. In July 2012CERN, the European laboratory for particle physics, announced the detection of a particle consistent with the Higgs boson.Nuclear Physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those in nuclear medicine and magnetic resonance imaging, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology.University PhysicsAstrophysics and Physical CosmologyAstrophysics and astronomy are the application of the theories and methods of physics to the study of stellar structure, stellar evolution, the origin of the solar system, and related problems of cosmology. Because astrophysics is a broad subject, astrophysicists typically apply many disciplines of physics, including mechanics, electromagnetism, statistical mechanics, thermodynamics, quantum mechanics, relativity, nuclear and particle physics, and atomic and molecular physics.The discovery by Karl Jansky in 1931 that radio signals were emitted by celestial bodies initiated the science of radio astronomy. Most recently, the frontiers of astronomy have been expanded by space exploration. Perturbations and interference from the earth's atmosphere make space-based observations necessary for infrared, ultraviolet, gamma-ray, and X-ray astronomy.Physical cosmology is the study of the formation and evolution of the universe on its largest scales. Albert Einstein's theory of relativity plays a central role in all modern cosmological theories. In the early 20th century, Hubble's discovery that the universe was expanding, as shown by the Hubble diagram, prompted rival explanations known as the steady state universe and the Big Bang.The Big Bang was confirmed by the success of Big Bang nucleo-synthesis and the discovery of the cosmic microwave background in 1964. The Big Bang model rests on two theoretical pillars: Albert Einstein's general relativity and the cosmological principle (On a sufficiently large scale, the properties of the Universe are the same for all observers). Cosmologists have recently established the ΛCDM model (the standard model of Big Bang cosmology) of the evolution of the universe, which includes cosmic inflation, dark energy and dark matter.Current research frontiersIn condensed matter physics, an important unsolved theoretical problem is that of high-temperature superconductivity. Many condensed matter experiments are aiming to fabricate workable spintronics and quantum computers.In particle physics, the first pieces of experimental evidence for physics beyond the Standard Model have begun to appear. Foremost among these are indications that neutrinos have non-zero mass. These experimental results appear to have solved the long-standing solar neutrino problem, and the physics of massive neutrinos remains an area of active theoretical and experimental research. Particle accelerators have begun probing energy scales in the TeV range, in which experimentalists are hoping to find evidence for the super-symmetric particles, after discovery of the Higgs boson.Theoretical attempts to unify quantum mechanics and general relativity into a single theory1 Physics 物理学of quantum gravity, a program ongoing for over half a century, have not yet been decisively resolved. The current leading candidates are M-theory, superstring theory and loop quantum gravity.Many astronomical and cosmological phenomena have yet to be satisfactorily explained, including the existence of ultra-high energy cosmic rays, the baryon asymmetry, the acceleration of the universe and the anomalous rotation rates of galaxies.Although much progress has been made in high-energy, quantum, and astronomical physics, many everyday phenomena involving complexity, chaos, or turbulence are still poorly understood. Complex problems that seem like they could be solved by a clever application of dynamics and mechanics remain unsolved; examples include the formation of sand-piles, nodes in trickling water, the shape of water droplets, mechanisms of surface tension catastrophes, and self-sorting in shaken heterogeneous collections.These complex phenomena have received growing attention since the 1970s for several reasons, including the availability of modern mathematical methods and computers, which enabled complex systems to be modeled in new ways. Complex physics has become part of increasingly interdisciplinary research, as exemplified by the study of turbulence in aerodynamics and the observation of pattern formation in biological systems.Vocabulary★natural science 自然科学academic disciplines 学科astronomy 天文学in their own right 凭他们本身的实力intersects相交,交叉interdisciplinary交叉学科的,跨学科的★quantum 量子的theoretical breakthroughs 理论突破★electromagnetism 电磁学dramatically显著地★thermodynamics热力学★calculus微积分validity★classical mechanics 经典力学chaos 混沌literate 学者★quantum mechanics量子力学★thermodynamics and statistical mechanics热力学与统计物理★special relativity狭义相对论is concerned with 关注,讨论,考虑acoustics 声学★optics 光学statics静力学at rest 静息kinematics运动学★dynamics动力学ultrasonics超声学manipulation 操作,处理,使用University Physicsinfrared红外ultraviolet紫外radiation辐射reflection 反射refraction 折射★interference 干涉★diffraction 衍射dispersion散射★polarization 极化,偏振internal energy 内能Electricity电性Magnetism 磁性intimate 亲密的induces 诱导,感应scale尺度★elementary particles基本粒子★high-energy physics 高能物理particle accelerators 粒子加速器valid 有效的,正当的★discrete离散的continuous 连续的complementary 互补的★frame of reference 参照系★the special theory of relativity 狭义相对论★general theory of relativity 广义相对论gravitation 重力,万有引力explicit 详细的,清楚的★quantum field theory 量子场论★condensed matter physics凝聚态物理astrophysics天体物理geophysics地球物理Universalist博学多才者★Macroscopic宏观Exotic奇异的★Superconducting 超导Ferromagnetic铁磁质Antiferromagnetic 反铁磁质★Spin自旋Lattice 晶格,点阵,网格★Society社会,学会★microscopic微观的hyperfine splitting超精细分裂fission分裂,裂变fusion熔合,聚变constituents成分,组分accelerators加速器detectors 检测器★quarks夸克lepton 轻子gauge bosons规范玻色子gluons胶子★Higgs boson希格斯玻色子CERN欧洲核子研究中心★Magnetic Resonance Imaging磁共振成像,核磁共振ion implantation 离子注入radiocarbon dating放射性碳年代测定法geology地质学archaeology考古学stellar 恒星cosmology宇宙论celestial bodies 天体Hubble diagram 哈勃图Rival竞争的★Big Bang大爆炸nucleo-synthesis核聚合,核合成pillar支柱cosmological principle宇宙学原理ΛCDM modelΛ-冷暗物质模型cosmic inflation宇宙膨胀1 Physics 物理学fabricate制造,建造spintronics自旋电子元件,自旋电子学★neutrinos 中微子superstring 超弦baryon重子turbulence湍流,扰动,骚动catastrophes突变,灾变,灾难heterogeneous collections异质性集合pattern formation模式形成University Physics2 Classical mechanics 经典力学IntroductionIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the oldest and largest subjects in science, engineering and technology.Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. Besides this, many specializations within the subject deal with gases, liquids, solids, and other specific sub-topics.Classical mechanics provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light. When the objects being dealt with become sufficiently small, it becomes necessary to introduce the other major sub-field of mechanics, quantum mechanics, which reconciles the macroscopic laws of physics with the atomic nature of matter and handles the wave–particle duality of atoms and molecules. In the case of high velocity objects approaching the speed of light, classical mechanics is enhanced by special relativity. General relativity unifies special relativity with Newton's law of universal gravitation, allowing physicists to handle gravitation at a deeper level.The initial stage in the development of classical mechanics is often referred to as Newtonian mechanics, and is associated with the physical concepts employed by and the mathematical methods invented by Newton himself, in parallel with Leibniz【莱布尼兹】, and others.Later, more abstract and general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances were largely made in the 18th and 19th centuries, and they extend substantially beyond Newton's work, particularly through their use of analytical mechanics. Ultimately, the mathematics developed for these were central to the creation of quantum mechanics.Description of classical mechanicsThe following introduces the basic concepts of classical mechanics. For simplicity, it often2 Classical mechanics 经典力学models real-world objects as point particles, objects with negligible size. The motion of a point particle is characterized by a small number of parameters: its position, mass, and the forces applied to it.In reality, the kind of objects that classical mechanics can describe always have a non-zero size. (The physics of very small particles, such as the electron, is more accurately described by quantum mechanics). Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional degrees of freedom—for example, a baseball can spin while it is moving. However, the results for point particles can be used to study such objects by treating them as composite objects, made up of a large number of interacting point particles. The center of mass of a composite object behaves like a point particle.Classical mechanics uses common-sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as where an object is in space and its speed. It also assumes that objects may be directly influenced only by their immediate surroundings, known as the principle of locality.In quantum mechanics objects may have unknowable position or velocity, or instantaneously interact with other objects at a distance.Position and its derivativesThe position of a point particle is defined with respect to an arbitrary fixed reference point, O, in space, usually accompanied by a coordinate system, with the reference point located at the origin of the coordinate system. It is defined as the vector r from O to the particle.In general, the point particle need not be stationary relative to O, so r is a function of t, the time elapsed since an arbitrary initial time.In pre-Einstein relativity (known as Galilean relativity), time is considered an absolute, i.e., the time interval between any given pair of events is the same for all observers. In addition to relying on absolute time, classical mechanics assumes Euclidean geometry for the structure of space.Velocity and speedThe velocity, or the rate of change of position with time, is defined as the derivative of the position with respect to time. In classical mechanics, velocities are directly additive and subtractive as vector quantities; they must be dealt with using vector analysis.When both objects are moving in the same direction, the difference can be given in terms of speed only by ignoring direction.University PhysicsAccelerationThe acceleration , or rate of change of velocity, is the derivative of the velocity with respect to time (the second derivative of the position with respect to time).Acceleration can arise from a change with time of the magnitude of the velocity or of the direction of the velocity or both . If only the magnitude v of the velocity decreases, this is sometimes referred to as deceleration , but generally any change in the velocity with time, including deceleration, is simply referred to as acceleration.Inertial frames of referenceWhile the position and velocity and acceleration of a particle can be referred to any observer in any state of motion, classical mechanics assumes the existence of a special family of reference frames in terms of which the mechanical laws of nature take a comparatively simple form. These special reference frames are called inertial frames .An inertial frame is such that when an object without any force interactions (an idealized situation) is viewed from it, it appears either to be at rest or in a state of uniform motion in a straight line. This is the fundamental definition of an inertial frame. They are characterized by the requirement that all forces entering the observer's physical laws originate in identifiable sources (charges, gravitational bodies, and so forth).A non-inertial reference frame is one accelerating with respect to an inertial one, and in such a non-inertial frame a particle is subject to acceleration by fictitious forces that enter the equations of motion solely as a result of its accelerated motion, and do not originate in identifiable sources. These fictitious forces are in addition to the real forces recognized in an inertial frame.A key concept of inertial frames is the method for identifying them. For practical purposes, reference frames that are un-accelerated with respect to the distant stars are regarded as good approximations to inertial frames.Forces; Newton's second lawNewton was the first to mathematically express the relationship between force and momentum . Some physicists interpret Newton's second law of motion as a definition of force and mass, while others consider it a fundamental postulate, a law of nature. Either interpretation has the same mathematical consequences, historically known as "Newton's Second Law":a m t v m t p F ===d )(d d dThe quantity m v is called the (canonical ) momentum . The net force on a particle is thus equal to rate of change of momentum of the particle with time.So long as the force acting on a particle is known, Newton's second law is sufficient to。
北大教授推荐——对我最有影响的几本书北京大学党委宣传部收集到了一部分教授的治学感言,学者们在其中都谈到了对自己最有影响的几本书。
图书馆将这些书目汇总起推荐给读者。
安平秋北京大学中文系教授题名责任者史记司马迁管子房玄龄注刘续增注论语孔子杨伯峻杨逢彬注译牛虻艾·丽·伏尼契(E.L.Voynich) 李俍民译古文观止吴楚材吴调侯选蔡运龙北京大学城市与环境学院教授题名责任者牛虻艾·丽·伏尼契(E.L.Voynich) 李俍民译毛泽东选集毛泽东哥德尔、艾舍尔、巴赫集异璧之大成侯世达郭维德等译地理学性质的透视R.哈特向黎樵译地理学中的解释大卫·哈维高泳源等译曹凤岐北京大学光华管理学院教授题名责任者矛盾论毛泽东实践论毛泽东资本论马克思中国近代史范文澜辩证唯物主义和历史唯物主义艾思奇曹维孝北京大学化学与分子工程学院教授题名责任者水浒传施耐庵,罗贯中李永祜点校居里夫人卢永建编译钢铁是怎样炼成的奥斯特洛夫斯基贵族之家屠格涅夫丽尼译牛虻艾·丽·伏尼契(E.L.Voynich) 李俍民译饥饿岛,死亡岛--日美瓜岛战记实南言昌增益北京大学生命科学学院教授题名责任者孙子兵法孙武道德经老子论语孔子 杨伯峻, 杨逢彬注译The Structure of Scientific RevolutionsThomas S. Kuhn A Study of HistoryToynbee, Arnold Joseph 题名责任者Qualitative Chemical Analysis of Inorganic Substances Noyes, Arthur A.Textbook of Quantitative Inorganic Analysis Kolthoff, I. M.大学普通化学付鹰定性分析张锡瑜化学元素的发现M. E. 韦克思 黄素封译题名责任者钢铁是怎样炼成的奥斯特洛夫斯基微积分学教程菲赫 金果尔茨 杨弢亮, 叶彦谦译自然哲学的数学原理牛顿 赵振江译朗道物理学丛书朗道·栗弗席兹A treatise on analytical dynamicsPars, L. A.题名责任者华家的 儿子陈伯吹居里夫人传艾芙· 居里 贾文浩, 贾文渊, 贾令仪译绞索套着脖子时的报告伏契克刘辽逸译原子物理学史包尔斯基 卢鹤绂等译Particle AcceleratorsM. Stanley Livingston,John P. Blewett.题名责任者陶庵梦忆張岱儒林外史吴敬梓文史通义章学诚国故论衡章太炎野 草鲁迅题名责任者爱因斯坦文集第一卷爱因斯坦 许良英,范岱年编译爱因 斯坦文集第二卷爱因斯坦 许良英,范岱年编译科学史及其与哲学和宗教的关系W· C· 丹 皮尔 李珩译常文保 北京大学化学与分子工程学院 教授陈平原 北京大学中文系 教授陈滨 北京大学工学院 教授陈佳洱 北京大学物理学院 教授陈庆云 北京大学政府管理学院 教授系统科学许国志Public policy analysis : an introductionDunn, William N.题名责任者钢铁是怎样炼成的奥斯特洛夫斯基毛泽东选集毛泽东力学朗道科学研究的艺术W.I.B.贝弗里奇 陈捷译Quantitative SeismologyAki, Keiiti 题名责任者法的形而上学原理 权利的科学康德 沈叔平译法哲 学原理黑格尔(G.W.F.Hegel) 范扬,张企泰译1844年经济学-哲学手稿马克思 刘丕坤 译论犯罪与刑罚贝卡里 亚 黄风译犯罪构成的一般学说特拉伊宁题名责任者毛泽东选集毛泽东Higher Education In Transition :A Historyof American Colleges and UniversitiesBrubacher, John Seiler 大学的功用Clark Kerr 陈学飞等译老子道德经王弼 注鲁滨孙漂流记丹尼尔·笛福 陈健健译题名责任者毛泽东 选集毛泽东大众哲学艾思奇古文观止吴楚材, 吴调侯编选智囊补冯梦龙辑管理学哈罗德·孔茨, 海因茨·韦里克 郝国华等译题名责任者红楼梦曹雪芹水浒传施耐庵,罗贯中 李永祜点校西游记吴承恩陈晓非 北京大学地球 与空间科学学院 教授陈兴良 北京大学法学院 教授陈占安 北京大学马克思主义学院 教授陈学飞 北京大学教育学院 教授陈志达 北京大学化学与分子工程学院 教授程玉华 北京大学信 息科学技术学院 教授题名责任者毛泽东选集毛泽 东第三次浪潮托夫勒孙 子兵法孙武艳阳天浩然三国演义罗贯中 沈伯俊点校题名责任者毛泽东选集毛泽东新华字典新华辞书社编写现代英汉词典外语教学与研究 出版社词典编辑室编题名责任者The art of computer programmingKnuth, Donald Ervin Computability: An Introduction toRecursive Function Theory Cutland, puters and Intractability: A Guide tothe Theory of NP-Completeness Garey, Michael R Data Structures and Network AlgorithmTarjan, Robert E Surely You’re Joking, Mr. FeynmanR·费曼 吴程远译题名责任者钢铁是这样炼成的 奥斯特洛夫斯基的一生温格罗夫, 爱弗罗斯著 谷鸣, 伊信译中国革命和中国共 产党毛泽东Ranganathan, S. R (Shiyali Ramamrita)题名责任者迟惠生 北京大学信息科学技术学院 教授戴龙基 北京大学图书馆 研究员丁明孝 北京大学生命科学学院 教授丛京生 北京大学信息科学技术学院 讲座教授The five laws of library science西游记吴承恩艾·丽·伏尼契(E.L.Voynich) 李俍民译唐诗 三百首蘅塘退士编选 胡可先注评宋 词三百首上彊村民编选 诸葛忆兵注评题名责任者实践论毛泽东矛盾论毛泽东题名责任者量子 力学厡理P. A. M. 狄拉克著 陈咸亨译QUANTUM MECHANICSCohen-Tannoudji, Claude Atomic and Laser Spectroscopy 科尼(A. Corney)著 邱元武等译The Dynamics of Spectroscopic Transitions Macomber, James D.题名责任者科学发现纵横谈王梓坤物种起源达尔文著 ;周建人 叶笃庄 方宗熙 译The Old Man and the SeaErnest Hemingway Wonderful life-The Burgess Shale and theNature of HistoryStephen Jay Gould Embryology: Constructingthe organism题名责任者青春之歌杨沫生物进化张昀生態学からみた自然吉良竜夫题名责任者中国史纲要翦伯赞世界通史(中古部分)周一良,吴于廑世界通史(近代部分 )周一良,吴于廑牛虻董太乾 北 京大学信息科学技术学院 教授董熙平 北京大学地球与空间科学学院 教授丁伟岳 北京大学数学学院 教授方连庆 北京大学国际关系学院 教授方精云 北京大学环境学院生态学 教授Scott F. Gilbert and Anne M. Raunio (eds)高崇文 北京大学考 古文博学院 教授题名责任者古史 辨顾颉刚观堂集林王国维十三经注疏阮元清经解阮元 王先谦編清经解续编王先谦先秦两汉考古学论集俞 伟超题名责任者罗伯森(Rober tson,P.)著 杨福家等译物理学与哲学 现代科学中的革命W.海森堡著 范岱年译爱因斯坦文集爱因斯坦著 许良英,范岱年编译Molecular magnetismKahn, Olivier 相同与不同洛德·霍夫曼著 李荣生等译题名责任者世界史纲韦尔斯著 蔡慕晖 蔡希陶译马克思恩格斯全集 [著作 卷] 第一卷马克思 恩格斯从 高卢到戴高乐张芝联西 方哲学史罗素著 何兆武李约瑟译笑 傲江湖金庸题名责 任者文史通义章学诚观堂集林王国维艺境宗白 华空间的驰想林庚唐诗论丛陈贻焮题名责任者科学 史及其与哲学和宗教的关系丹皮尔, W. C. D .时间简史史蒂芬·霍金 列纳德·蒙洛迪诺著 吴忠超译CausalityJudea Pearl 波普尔(K.R.Popper)著 沈恩明缩编猜想与反驳玻尔研究所的早年岁月高毅 北京大学历史系 教授高松 北京大学化学与分子工程学院 教授耿直 北京大学数学 科学学院 教授葛晓音 北京大学中文 系 教授Modern EpidemiologyRothman, Kenneth J.题名责任者Principles ofOptics光学原理马科斯 ·玻恩, 埃米尔·沃耳夫著 杨葭荪译科学随笔经典(丛书)黎先 耀贝尔实验室 现代高科技的摇篮阎康年卡文迪什实验室 现代科学革命的圣地阎康年爱因斯坦的圣经萨缪尔等著 李斯 马永波译题名责任者Treatise on Inorganic chemistryRemy, H.确定性的 终结 时间、混沌与新自然法则伊利亚·普利高津著 湛敏译PCR 传奇 一个生物技术的故事保罗·拉比诺著 朱玉贤译虚实世界 计算机仿真如何改变科学的疆域约翰·L·卡斯蒂著 王千祥,权利宁译完美的对称 富勒烯的意外发现吉姆 ·巴戈特著 李涛 曹志良译超越时空 通过平行宇宙、时间卷曲和第十维度的科 学之旅加来道雄著 刘玉玺 曹志良译题名责任者Wind Effects onStructures, 3rd edLow-speed WindTunnel Testing,2nd ed.流 体力学概论L.普朗特 等 著,郭永怀 陆士嘉译流体力学吴望一Boundary LayerTheory, seventh ed.题名责任者战 争与和平列夫·托尔斯泰怎样 识星程廷芳著 南京大学天文系修订Max,Born 钢铁是怎样 炼成的奥斯特洛夫斯基Ermann Schlichting William H.Rae, Jr. & Alan Pope 龚旗煌 北京大学物理学院 教授顾 志福 北京大学工学院 教授顾镇南 北京大学化学与分子工程学院 教授Emil Simiu & Robert H. Scanlan 郭之虞 北京大学物理学院 教授物理学的进化艾·爱因斯坦(A.Einstein),利·英费尔德(L.Infeld)著周肇威译为什么不是最好的吉米·卡特著版本图书馆编译室译海闻北京大学中国经济研究中心教授题名责任者红岩罗广斌,杨益言林海雪原曲波毛泽东选集毛泽东资本论马克思经济学保罗·萨缪尔森, 威廉·诺德豪斯韩汝琦北京大学信息科学技术学院教授题名责任者理论物理学教程(丛书)Л·д·朗道,E. M.栗弗席兹著李俊峰译半导体物理学黄昆谢希德Dynamical Theory of Crystal Lattices Born, Max离子晶体中的电子过程莫特,N.F.格尼,R.W.著潘金声,李文雄译吴大猷文选吴大猷郝守刚北京大学地球与空间科学学院教授题名责任者词综朱彝尊,汪森古代汉语王力生物进化张昀物种起源达尔文著周建人叶万庄方宗熙译Ever Since Darwin Gould Stephen Jay.何芳川北京大学历史系教授题名责任者家庭私有制和国家的起源恩格斯著张仲实译拿破仑传叶·维·塔尔列著任田升, 陈国雄译大卫·科波菲尔查尔斯·狄更斯著庄绎传译尼赫鲁自传尼赫鲁著毕来译资治通鉴司马光胡家峦北京大学外国语学院教授题名责任者十七世纪英国文学杨周翰美妙的和谐:毕达哥拉斯宇宙论与文艺复兴时期诗学图像研究:文艺复兴艺术中的人文主题西方建筑的意义诺贝格-舒尔茨 (Norberg-Schultz, Christian)著 李路珂 欧阳恬之译失乐园弥尔顿(J. Milton)著 朱维之译题名责任者四书通译赵定宪 赵腾译庄子庄子理想国柏拉图著 刘勉 郭永刚译纯粹理性批判康德著 胡仁 源译哲学问题罗素著 何兆武译题名责任者牛虻艾·丽·伏尼契(E.L.Voynich)著 李俍民译大卫·科波菲尔查尔斯·狄更斯原著 安妮·德赫拉夫改写 袁宪军注约翰·克里斯朵夫罗曼·罗兰著 傅雷译工程控制论钱学森, 宋健著运动稳定性一般理论李亚普诺夫题名责任者A Course of Modern AnalysisWhittaker, E. T.Modern Developmemts in Fluid Dynamics Goldstein, S.An Introduction to Fluid DynamicsBatchelor, G. K.Vectors, Tensors, and the Basic Equations of Fluid Mechanics Aris, Rutherford.TurbulenceHinze J.O.题名责任者三国演义罗贯中著 沈伯俊校点唐诗三百首蘅塘 退士编选 胡可先注评辨证唯物主义历史唯物主义艾思奇主编列宁全集列宁让历史来审判罗伊·梅德韦 杰夫著 何宏江等译题名责任者数学万花镜胡·施坦豪斯(H.Steinhans)著 裘光明译直观几何 D. 希尔伯特, S. 康福森著 王联芳译黄琳 北京大学工学院 教授胡军 北京大学哲学系 教授姜伯驹 北京大学数学科学学院教授黄永念 北京大学工学院 教授黄宗良 北京大学国际关系学院 教授数学是什么柯朗(Courant,R.),罗宾斯(Robbins,H.)著左平张饴慈译怎样解题波利亚(G. Polya)著阎育苏译姜明安北京大学法学院教授题名责任者战斗的青春雪克论法的精神孟德斯鸠(Montesquieu)著申林编译中国行政法总论马军硕英宪精义戴雪著雷宾南译制度经济学柯武刚史漫飞著韩朝华译蒋绍愚北京大学中文系教授题名责任者论语朱熹集注崔存明校订老子老子楚辞屈原唐诗别裁沈德潜选注汉语史稿王力著金长文北京大学化学与分子工程学院教授题名责任者围城钱钟书歌德巴赫猜想徐迟著三国演义罗贯中著沈伯俊校点论语朱熹集注崔存明校订红楼梦曹雪芹寇元北京大学化学与分子工程学院教授题名责任者量子史话霍夫曼 B. (Hobbmann,Banesh) 著New Synthesis with Carbon Monoxide Falbe J. 主编王杰译Advanced Inorganic Chemistry F. A. Cotton and G. Wilkinson非晶态固体物理学R. 泽仑黄畇译The Surface Science of Metal Oxides V. E. Henrich and P. A. Cox黎乐民北京大学化学与分子工程学院教授题名责任者化学奇谈法布尔,J. H. (Fabre, J. H.) 著无脚飞将军波列伏依原著施瑛改写实践论毛泽东著矛盾论毛泽东著量子力学原理狄拉克著陈咸亨译题名责任者钢铁是怎样炼成的奥斯特洛夫斯基中国通史周一良雷锋日记雷锋 著毛泽东选集毛泽 东著Treatise on Analytical ChemistryKolthoff, I. M. (Izaak Maurits)题名责任者牛棚杂忆季羡林著斯大林德·安· 沃尔科戈诺夫著 张慕良译未来之路比尔·盖茨著谁说大象不能跳舞郭士纳著 张秀琴 音正权译悲惨世界维克多·雨果著 郑向菲译注题名责任者经济分析史约瑟夫·熊彼特著 朱泱等译新教伦理与 资本主义精神马克斯·韦伯著 彭强 黄晓京译国史大纲钱穆著花间集赵崇祚辑宽容亨德里克·威廉·房龙著 马晗 治梅编译题名责任者资本论马克思 中共中央马克思恩格斯列宁斯大林著作编译局译钢铁是怎样炼成的尼·奥斯特洛夫斯基著 刘心语译通往奴役之路弗里德里希·奥古斯特·冯·哈耶克著 王明毅等译题名责任者Quantum chemistryLevine, Ira N.Methods of molecular quantum mechanicsMcWeeny, R.Modern quantum chemistry : introductionto advanced electronic structure theorySzabo, Attila 鹿鼎记金庸天龙八部金庸厉以宁 北京大学光华管理学院 教授李克安 北京大学化学与分子工程学院 教授李晓明 北京大学信息科学技术学院 教授刘文剑 北 京大学化学与分子工程学院 教授刘晓为 北京大学天文学系 教授刘伟 北 京大学经济学院 教授歌德谈话 1823-1832爱克曼辑录 朱光潜译中国人性论 史先秦篇徐复观著题名责任者莎士比亚戏剧全集莎士比亚 著朱生豪译三国演义罗贯中著 沈伯俊校点红楼梦曹雪芹诺顿英国文学选读Abrams, M. H.题名责任 者Electrochemical methods : fundamentalsand applications Bard, Allen J.The solid state : an introduction to thephysics of crystals for students of physics,materials science, and engineering Rosenberg, H. M.The Quintessence of Irving LangmuirAlbert Rosenfeld 梁实秋散文精品梁实秋题名责任者毛泽东选集毛泽东高等数学讲义樊映川编生物化学沈同中国人史 纲柏杨题名责任者论语朱熹集 注 崔存明校订庄子郭象注 陆德明音义 崔存明校订题名责任者易经今译孙振声编著庄子今注今译陈鼓应注译约翰克 里斯朵夫罗曼·罗兰著(Jean-Christophe Romain Rolland)著傅雷译爱因斯坦文集爱因斯坦著 许良英 范岱年编译批判哲学的批判康德述评 李泽厚译刘忠范 北京大学化学与分子工程学院 教授刘意青 北京 大学外国语学院 教授马伯强 北京大学物理学院 教授罗明 北京大学生命科学学院 教授罗志田 北京大学历史系 教授马季铭 北京大学化学与分子工程学院 教授儒勒·凡尔纳的科幻小说儒勒·凡尔纳著大学普通化学傅鹰编马戎北京大学社会学系教授题名责任者万历十五年黄仁宇著乡土中国费孝通怎么办?车尔尼雪夫斯基著魏玲译钢铁是怎样炼成的尼·奥斯特洛夫斯基著刘心语译梅宏北京大学信息科学技术学院教授题名责任者封神演义许仲琳著三国演义罗贯中著哥德巴赫猜想徐迟孟杰北京大学物理学院教授题名责任者史记司马迁撰裴骃集解司马贞索引张守节正义华罗庚传顾迈南著少年维特的烦恼歌德著杨武能等译量子力学曾谨言著The nuclear many-body problem Ring, Peter闵维方北京大学教育学院教授题名责任者资本论马克思中共中央马克思恩格斯列宁斯大林著作编译局译唯物主义与经验批判主义对一种反动哲学的批判列宁著曹葆华译大教学论夸美纽斯著傅任敢译组织马奇,西蒙著邵冲译论人力资本投资西奥多·W·舒尔茨著吴珠华等译宁骚北京大学政府管理学院教授题名责任者毛泽东选集毛泽东著邓小平文选邓小平著孟子万丽华蓝旭译注史记司马迁撰裴骃集解司马贞索引张守节正义呐喊鲁迅著欧阳颀北京大学物理学院教授题名责任者Self- organization in nonequilibriumsystems : from dissipative structures toorder through fluctuationsNicolis, G.沉默的大多数 美国工人阶级家庭生活莉莲·B. 露宾著 汪泽青 张卫红译How Nature worksBak, P. (Per)The end of ScienceHorgan, John The dream of a final theorySteven Weinberg 题名责任者十万个为什 么路明等编徐霞客游记徐宏祖著普通地理学原理С.В. 卡列斯尼克著 唐永鑾 王正宪译黄土与环 境刘东生等著Sedimentary environments and faciesReading, H. G.题名责任者Singular integrals and differentiabilityproperties of functions Stein, Elias M.Theory of Function SpacesTriebel, Hans Ten Lectures on WaveletsDaubechies, Ingrid Harmonic analysis on symmetric spacesand applicationsTerras, Audrey 中国文学史知识丛书王力主编题名责任者战争与和平托尔斯泰,Л.Н. (Толсто,Л.Н.) 著 高植译约翰 ·克里斯朵夫罗曼·罗兰著 傅雷译热力学王竹溪著Diffraction physicsCowley,J.M.(John Maxwell)Electron microscopy of thin crystalsHirsch,P.B. (Peter Bernhard)题名责任者钢铁是怎样炼成的尼·奥斯特洛夫斯基著 刘心语译远离莫斯科的地方阿札耶夫著 刘辽逸, 谢素台译论共产党员的 修养 一九三九年七月在延安马列学院的讲演刘少奇 著协 同学—大自然构成的奥秘赫尔曼·哈肯著 凌复华译老人与海海明威著 李锡胤译潘懋 北京大学地球与空间科学学院 教授彭练矛 北京大学物理学院 教授濮祖荫 北京大学地球与空间学院 教授彭立中 北京大学数学科学学院 教授题名责任者唐宋词选注唐圭璋编著英国工人阶级的形成E. P. 汤普森著 钱乘旦等译简爱夏洛蒂·勃朗特著 戴侃译英华大辞典郑易里等编世界通史王斯德 主编题名责任者物理学的进化艾·爱因斯坦(A.Einstein),利·英费尔德(L.Infeld)著周肇威译三国 演义罗贯中著毛泽东选集毛泽东著史记司马迁撰 裴骃集解 司马贞索引 张守节正义世界史海斯,穆恩,韦兰著 中央民族学院研究室译题名责任者论语朱熹集注 崔存明校订圣经美学黑格尔著 朱光潜译约翰·克里斯朵夫罗曼·罗兰著 傅雷译拿 破仑传布里昂著 郁飞译题名责任者三国志陈寿 撰纪念白求恩 为人民服务毛泽东愚公移山毛泽东自然辨证法徐治立主编 徐治立等编著BiochemistryCampbell,Mary K 题名责任者英汉化学化工词汇化学工业出版社辞书编 辑部编Electrochemical methods : fundamentalsand applicationsAllen J. Bard and Larry R. Faulkner 金庸全集金庸李煜集李煜著 王晓枫解评Electrochemistry on liquid/liquid interfaces Vanysek, P.秦国刚 北京大学物理学院 教 授钱乘旦 北京大学历史系 教 授邵元华 北京大学化学与分子工程学院 教授任光宣 北京大学俄文 系 教授茹炳 根 北京大学生命科学学院 教授题名责任者道德经李耳著易经苏勇点校达尔文进化论全集第三卷物种起源Ch.达尔文著周建人等译自然界的分析几何湍流欣茨(Hinze,J.O)著周光魏中磊译题名责任者Jane Eyre Bront, CharlotteStyle in fiction : a linguistic introduction to English fictional prose Leech, Geoffrey N.Narrative fiction : contemporary poetics Rimmon-Kenan, Shlomith.Literary theory : an introduction Eagleton, Terry红岩罗广斌杨益言著题名责任者哥德尔、艾舍尔、巴赫集异璧之大成霍夫施塔特著郭维德等译竞赛论与经济行为约翰·冯·诺依曼, 奥斯卡·摩根斯特恩著王建华顾玮琳译资产选择:投资的有效分散化哈里·马克威茨著刘军霞张一驰译投资组合理论与资本市场威廉 F. 夏普著胡坚译Continuous-time finance Merton, Robert C题名责任者原子在我家中费米夫人著何芬奇译生命是什么埃尔温·薛定谔著罗来鸥, 罗辽复译The double helix :a personal account of the discovery of the structure of DNA Watson, James D.Molecular biology of the cell Alberts, BruceProtein crystallography Blundell, T. L.题名责任者林肯·传艾米尔·路德维希著富强译爱迪生传 Thomas Alva Edison 1847-1931李其荣编著A Course of Study in Chemical PrinciplesThe nature of the chemical bond and the structure of molecules and crystals : an introduction to modern structural chemistry Pauling, Linus申丹北京大学外国语学院教授史树中北京大学光华管理学院教授佘振苏北京大学工学院教授唐有祺北京大学化学与分子工程学院教授苏晓东北京大学生命科学学院教授The Crystalline stateBragg, William Henry, Sir SymmetryWeyl, Hermann 题名责任者海底两万里凡尔纳著 曾觉之译在地球之外康·齐奥尔科夫斯基著 麦林等译血字的研究阿·柯南道尔著 丁钟华, 袁棣华译趣味数学柯尔詹姆斯基 张继武, 程韬译场论Л. 朗道, Е. 栗弗席兹著 任朗, 袁炳南译题名责任者三国演义罗贯中著 沈伯俊校点国家间政治 寻求权力与和平的斗争摩根索著 汤普森修订 徐昕等译毛泽东选集毛泽东战 争与和平列夫·托尔斯泰牛虻艾·丽·伏尼契著 李俍民译题名责任者Mechanism and Theory in OrganicChemistry Lowry, Thomas H.A guidebook to mechanism in organicchemistry Sykes, Peter Advanced organic chemistryCarey, Francis A.The rise and fall of the great powersKennedy, Paul M.吾国与吾民林语堂原著 郑陀译题名责任者礼记钱玄等 注译乡土中国费孝通著共产党宣言马克 思, 恩格斯 成仿吾译经济与社会韦伯著 杭聪编译题名责任者论语朱熹集注 崔存明校订史记司马迁撰 裴骃集解 司马贞索引 张守节正义贞观政要吴兢编著 王贵标点明夷待访录黄宗羲著红楼梦曹雪芹, 高鹗著 中国艺术研究院红楼梦研究所校注王剑波 北京大学化学与分子工程学院 教授田光善 北京大学物理学院 教授王缉思 北京大学国际关系学院 教授王天有 北京大学历史学系 教授王思斌 北京大学社会学系 教授题名责任者钢铁是怎样 炼成的尼·奥斯特洛夫斯基著 刘心语译牛虻艾·丽·伏尼契著 李俍民译追忆似水年 华M. 普鲁斯特著 李恒基, 徐继曾等译俄苏形式主义文论选托多罗夫编选 蔡鸿滨译文心雕龙刘勰著题名责任 者牛虻艾·丽·伏尼契著 李俍民译物质结构徐光宪编著比一千个太阳还亮 原子科 学家的故事容克著 钟毅,何纬译鲁迅的 杂文、散文与诗鲁迅傅雷家书傅雷著题名责任者钢铁是怎样 炼成的尼·奥斯特洛夫斯基著 刘心语译大学物理 讲义黄昆The Path To the Conception of The Junction TransistorW. Shockley居里夫 人传艾芙·居里著 贾文浩, 贾文渊, 贾令仪译毛泽东诗词集中共中央文献研究室编题名责任者论语朱熹集注 崔存明校订共产党宣言马克思, 恩格斯 成仿吾译鲁迅全集鲁迅著红楼梦曹雪芹 高 鹗著 中国艺术研究院红楼梦研究所校注恩格斯自然辩证法恩格斯题名责任者红楼梦曹雪芹 高鹗著 中国艺术研究院红楼梦研究所校注鲁迅杂文鲁迅卓娅和舒拉的故事柳·科斯莫杰米杨斯卡娅著 苏卓兴, 陶薰 仁, 毛蔚译数学与哲学张景中著钦定三希堂法帖王文融 北京大学外国语学院 教授王阳元 北京大学信息科学技术学院 教授王祥云 北京大学化学与 分子工程学院 教授吴瑾光 北京大学化学与分子 工程学院 教授温儒敏 北京大学中文系 教授文兰 北京大学数学科学学院 教授题名责任者物质结构徐光宪编著Fourier transform infrared spectroscopy Ferraro, John R.稀土徐光宪主编题名责任者高中教材《代数》小学教材《自然》红楼梦曹雪芹,高鹗著中国艺术研究院红楼梦研究所校注中国画论辑要周积寅编著题名责任者共产党宣言马克思恩格斯成仿吾译孟子朱熹集注崔存明校订大众哲学艾思奇著帝国主义与中国政治胡绳著《资本论》注释卢森贝著赵木斋翟松年译题名责任者Organolithium Methods Wakefield, B. J.题名责任者辞海辞海编辑委员会编纂事物的起源利普斯著汪宁生译徐霞客游记徐弘祖著褚绍唐, 吴应寿整理亚洲腹地旅行记斯文·赫定著大陆桥翻译社译宇宙发展史概论伊曼努尔·康德著全增嘏译题名责任者The mathematical theory of communication Shannon, Claude E.Spread spectrum systems Dixon, Robert C.Detection of signals in noise Whalen, Anthony D.Multiuser detection Verdu, SergioNear Shannon Limit Error-Correcting Coding and Decoding Berrou, C.;Glavieux, A.;Thitimajshima, P.吴树青北京大学经济学院教授席振峰北京大学化学与分子工程学院教授吴全德北京大学物理学院教授项海格北京大学信息科学技术学院教授夏正楷北京大学城市与环境学院教授。
a r X i v :q u a n t -p h /0107076v 2 30 S e p 2001Universal dynamical control of quantum mechanical decay:Modulation of thecoupling to the continuumA.G.Kofman and G.KurizkiDepartment of Chemical Physics,The Weizmann Institute of Science,Rehovot 76100,IsraelWe derive and investigate an expression for the dynam-ically modified decay of states coupled to an arbitrary con-tinuum.This expression is universally valid for weak tempo-ral perturbations.The resulting insights can serve as useful recipes for optimized control of decay and decoherence.PACS numbers:03.65.Ta,03.65.Xp,42.25.Kb,42.50.VkThe quantum Zeno effect (QZE),namely,the inhibi-tion of the decay of an unstable state by its (sufficientlyfrequent)projective measurements,has long been con-sidered a basic universal feature of quantum systems [1].Our general analysis [2]has revealed the inherent impos-sibility of the QZE for a broad class of processes,includ-ing spontaneous emission in open space,as opposed to the ubiquitous occurrence of the anti-Zeno effect (AZE),i.e.,decay acceleration by frequent projective measure-ments [3].Although realistic schemes may well approxi-mate such measurements [2,4,5],there is strong incentive for raising the question:Are projective measurements the most effective way of modifying the decay of an unsta-ble state?This question is prompted by two important results:(a)A landmark experiment has demonstrated,for the first time,both the QZE and AZE by repeated on-offswitching of the coupling between a nearly bound state and the continuum,using cold atoms that are ini-tially trapped in an optical-lattice potential [6].(b)It has been predicted that periodic coherent pulses,acting between the decaying level and an auxiliary one,can ei-ther inhibit or accelerate the decay into certain model reservoirs [7].In both [6]and [7],the repeated interrup-tion of the “natural”evolution is imperative for decay modification.In this paper we purport to substantially expand the arsenal of decay control,whether measurement-like (i.e.,accompanied by dephasing)or fully coherent.We de-rive a universal form of the decay rate of unstable states into any reservoir (continuum),modified by weak pertur-bations with arbitrary time dependence.The results of Refs.[2,3,6,7]are recovered as limiting cases of this uni-versal form.Our analysis can serve as a general recipe for optimized decay and decoherence suppression for quan-tum logic operations [8]or decay enhancement for the control of chaos or chemical reactions [9].Consider the decay of a state |e via its coupling to a system,described by the orthonormal basis {|j },which forms either a discrete or a continuous spectrum (or a mixture thereof).In its most general form,the totalHamiltonian is ˆH0+ˆV (t )+H 1(t ),where ˆH 0=¯h ωa |e e |+¯hjωj |j j |,(1)with ¯h ωa and ¯h ωj being the energies of |e and |j ,re-spectively;ˆV (t )=jV ej (t )|e j |+h.c.,(2)denoting the off-diagonal coupling of |e with the otherstates,which is dynamically modulated,so as to modifythe static limit of ˆVeffecting the natural decay process;andH 1(t )=¯h δa (t )|e e |+¯hjδj (t )|j j |,(3)standing for the adiabatic (diagonal)time-dependentperturbations of the energies of the initial (|e )and fi-nal (|j )states,e.g.,AC Stark shifts.We write the wave function of the system,with |e populated at t =0,as|Ψ(t ) =α(t )e −iωa t −i t0δa (t ′)dt ′|e+jβj (t )e −iωj t −i t 0δj (t ′)dt ′|j ,(4)the initial condition being |Ψ(0) =|e .Henceforth wetreat the generic case wherein the level shifts and thetemporal modulation of ˆV(t )are independent of j ,i.e.,δj (t )≡δf (t )and V je (t )≡˜ǫ(t )µje ,˜ǫ(t )being the modu-lation function (Fig.1–inset).Such factorized form of the modulation is commonly valid for weak or moderate time-dependent fields,which do not appreciably change the states of the continuum.One then obtains from the Schr¨o dinger equation that the amplitude α(t )obeys the exact integro-differential equation [10]˙α=−tdt ′ǫ∗(t )ǫ(t ′)Φ(t −t ′)e iωa (t −t ′)α(t ′).(5)Here Φ(t )=¯h −2 j |µej |2e −iωj (t )is the reservoir re-sponse (memory)function and the function ǫ(t )=˜ǫ(t )exp[−i t0δaf (t ′)dt ′],with δaf (t )=δa (t )−δf (t ),accounts for the modulation of either diagonal or off-diagonal elements of the unperturbed Hamiltonian.The assumption that the coupling (2)is a weak pertur-bation of (1)implies that α(t )varies sufficiently slowly with respect to the kernel of Eq.(5),since we then an-ticipate [cf.the validity condition (11)]decay rates muchsmaller than the rate of change of the reservoir response Φ(t ).One can thus make theapproximation α(t ′)≈α(t )on the right-hand side (rhs)of Eq.(5).Then one can solve Eq.(5)and represent the amplitude modulus of level |e in the form|α(t )|=exp[−R (t )Q (t )/2],(6)where we have introduced the fluence Q (t )= t0dτ|ǫ(τ)|2,and obtained the decay rate in the universal formR (t )=2π ∞−∞dωG (ω+ωa )F t (ω).(7)Here G (ω)=π−1Re ∞0dte iωt Φ(t )=¯h −2j |µej |2δ(ω−ωj )is the coupling spectrum,i.e.,the density of states weighted by the strength of the coupling to the contin-uum or reservoir;F t (ω)=|ǫt (ω)|2/Q (t ),with ǫt (ω)=(2π)−1/2 t 0ǫ(t ′)e iωt ′dt ′,is the (normalized to unity)spectrum of the modulation function ǫ(t )in the “win-dow”(0,t ).The result (6),(7)is valid to all orders of t ,i.e.,it keeps intact the interferences between the mod-ulated decay channels and their non-Markovian effects.We stress that Eqs.(6),(7)apply to the decay of super-posed statesm αm |e m (e.g.,in quantum information schemes),provided all of them decay and are modulated identically.We now consider some important consequences of the universal form (6),(7).The modulation spectrum F t (ω)is roughly characterized by its width νt and the frequency shift ∆t =dωωF t (ω).A modulation may strongly modify the decay rate (analogously to the QZE or AZE)whenever νt +|∆t |>∼ξ(ωa ),where ξ(ωa )is the charac-teristic spectral interval over which the weighted density of states G (ω)changes near ωa .In particular,if ωa is near the edge of the continuum (as for radiative decay in photonic crystals or vibrational decay in ion traps,molecules and solids),then ξ(ωa )is the distance between ωa and the edge [2](Fig.1a).Only in the opposite limit,νt +|∆t |≪ξ(ωa ),can one approximately set F t (ω)≈δ(ω)in Eq.(7),yielding P (t )≈exp[−R GR Q (t )],where R GR =2πG (ωa )is the extension of the Golden-Rule (GR)rate to the case of a time-dependent coupling .The modulation function ǫ(t )can be either random or regular (coherent)in time,as detailed below.Con-sider first the most general coherent amplitude and phase modulation (APM)of the quasiperiodic form,ǫ(t )= k ǫk e−iωk t.Here ωk (k =0,±1,...)are arbitrary dis-crete frequencies with the minimum spectral distance Ω.For a given function ǫ(t )one can obtain −iωk and ǫk as the poles and residues,respectively,of the Laplace trans-form ˆǫ(s ).If ǫ(t )is periodic with the period Ω,then ωk =k Ω,and ǫk become the Fourier components of ǫ(t ).For a general quasiperiodic ǫ(t ),one obtainsQ (t )=ǫ2c t +ǫ2ck =lλk λ∗le i (ωl −ωk )t−12πηk ηl.(9)Here ηk =ω−ωk ,whereas S (ηk t/2)=2sin 2(ηk t/2)/πtη2k is a sinc-function of ηk normalized to 1.12345Modulation period00.20.40.60.8123(b)aFIG.1.Decay modification by modulation [Eqs.(6),(7)].Inset:Schematic view of the temporal modulation of the shift of level e and its coupling to a continuum.(a)ωa is near a band edge of G (ω)=Cω1/2(ω+Γ)−1θ(ω),where θ(ω)is the unit step function;then a small phase shift (dashed peak)is more effective in reducing the decay rate R than large phase shifts φ≃π(dash-dotted peaks)or frequent measure-ments/random ǫ(t )(thin curve).(b)Decay rate R (in units of R GR )in case (a)with ωa =0.1Γ:reduction by PM [Eq.(10)](curve 1–φ=0.1,curve 2–φ=π)and frequent impulsive measurements [2](curve 3–QZE)as a function of perturba-tion period τ(in units of Γ−1).Curve 1gives the strongest reduction of R at a given τ.For t ≫Ω−1the first term on the rhs of (9)is a sum of peaks,whose spacings are much greater than their width 2/t .The fast oscillating second term is also peaked at ω=ωk ,but we then find that the ratio of the first to the second terms,and that of their counterparts in (8),is ∼(Ωt )−1≪1.In the long-time limit,we then ne-glect these fast oscillating terms and obtain from Eqs.(6)-(9)that P (t )=exp[−R (t )ǫ2c t ],where R (t )in Eq.(7)now involves F t (ω)≈ k |λk |2S (ηk t/2).For even longer times,exceeding the effective correlation (memory)time of the reservoir,t c ≡max k {1/ξ(ωa +ωk )},the functions S (ηk t/2)become narrower than the respective charac-teristic widths of G (ω)around ωa +ωk ,and one can set S (ηk t/2)≈δ(ηk ).Then Eq.(7)is reduced toR =2πk|λk |2G (ωa +ωk ),(10)which holds ifRt c ≪1.(11)This condition is well satisfied in the regime of interest,i.e.,weak coupling to essentially any reservoir,unless (forsome k)ωa+ωk is extremely close to a sharp feature in G(ω),e.g.,a band edge[11].Hence,the long-time limit of the general decay rate(7)under the APM is a sum of the GR rates,corresponding to the resonant frequencies shifted byωk,with the weights|λk|2.Formula(10)pro-vides a simple general recipe for manipulating the decay rate by APM.Its powerful generality allows for the opti-mized control of decay,not just for a single level,but also for band characterized by a spectral distribution P(ωa) (e.g.,inhomogeneous or vibrational spectrum).We can then chooseλk andωk in Eq.(10)so as to minimize the decay of(6)convoluted with P(ωa).The following limits of(10)will be now analyzed.(i)Monochromatic perturbation:Letǫ(t)=ǫ0e−iδaf t. Then R=2πG(ωa+∆),where∆=δaf=const is an AC Stark shift.In principle,such a shift may drasti-cally enhance or suppress R relative to R GR.It provides the maximal variation of R achievable with an exter-nal perturbation,since it does not involve any averag-ing(smoothing)of G(ω)incurred by the width of F t(ω): the modified R can even vanish,if the shifted frequency ωa+∆is beyond the cutofffrequency of the coupling, where G(ω)=0(Fig.1a,b).Conversely,the increase of R due to a shift can be much greater than that achiev-able with the AZE[2].In practice,however,AC Stark shifts are usually small for(CW)monochromatic per-turbations,whence pulsed perturbations should often be used,resulting in multipleωk shifts according to(10). (ii)Impulsive phase modulation(PM):Let the phase of the coupling amplitude jump by an amountφat times τ,2τ,....Such modulation can be achieved by a train of identical,equidistant,narrow pulses of nonresonant radiation,which produce pulsed AC Stark shiftsδaf(t) in(3).Nowǫ(t)=e i[t/τ]φ,where[...]is the integer part.One then obtains thatǫc=1and Q(t)=t.The decay is given by Eqs.(6)and(7),where F t(ω)can be obtained in a closed form.For sufficiently long times one can use Eq.(10).The poles and residues ofˆǫ(s)= (1−e−sτ)/[s(1−e iφ−sτ)]yieldωk=2kπ/τ−φ/τand |λk|2=4sin2(φ/2)/(2kπ−φ)2.For small phase shifts,φ≪1,the k=0peak dominates,|λ0|2≈1−φ2/12, whereas|λk|2≈φ2/4π2k2for k=0.In this case one can retain only the k=0term in Eq.(10)[unless G(ω) is changing very fast].Then the modulation acts as a constant shift∆=−φ/τ.With the increase of|φ|,the difference between the k=0and k=1peak heights diminishes,vanishing forφ=±π.Then|λ0|2=|λ1|2= 4/π2,i.e.,F t(ω)forφ=±πcontains two identical peaks symmetrically shifted in opposite directions(Fig.1a)[the other peaks|λk|2decrease with k as(2k−1)−2,totaling 0.19].The above features allow one to adjust the modulation parameters for a given scenario to obtain an optimal de-crease or increase of R.The PM scheme with a smallφis preferable near the continuum edge(Fig.1a,b),since it yields a spectral shift in the required direction(positive or negative).The adverse effect of k=0peaks in F t(ω)then scales asφ2and hence can be significantly reduced by decreasing|φ|.On the other hand,ifωa is near a symmetric peak of G(ω),R is reduced more effectively forφ≃π,as in Ref.[7],since the main peaks of F t(ω) atω0andω1then shift stronger withτ−1than the peak atω0=−φ/τforφ≪1.(iii)Amplitude modulation(AM)of the coupling arises, e.g.,for radiative-decay modulation due to atomic mo-tion through a high-Q cavity or a photonic crystal[12]or for atomic tunneling in optical lattices with time-varying lattice acceleration[6,13].Let the coupling be turned on and offperiodically,for the timeτ1andτ0−τ1,respec-tively,i.e.,ǫ=1for nτ0<t<nτ0+τ1andǫ=0for nτ0+τ1<t<(n+1)τ0(n=0,1,...).Now Q(t)in(6) is the total time during which the coupling is switched on.This case is also covered by Eq.(10),where the pa-rameters are now found to beǫ2c=τ1/τ0,ωk=2kπ/τ0, |λ0|2=τ1/τ0,|λk|2=(τ1/τ0)sinc2(kπτ1/τ0)(k=0).It is instructive to consider the limit whereinτ1≪τ0 andτ0is much greater than the correlation time of the continuum,i.e.,G(ω)does not change significantly over the spectral intervals(2πk/τ0,2π(k+1)/τ0).In this case one can approximate the sum(10)by the integral(7) with F t(ω)≈(τ1/2π)sinc2(ωτ1/2),characterized by the spectral broadening∼1/τ1(Fig.2–inset).Then Eq.(7)for R reduces to that obtained when ideal projective measurements are performed at intervalsτ1[2].Thus the AM scheme can imitate measurement-induced (dephasing)effects on quantum dynamics,if the inter-ruption intervalsτ0exceed the correlation time of the continuum.This indeed has been observed[6]for atom tunneling in optical lattices whose tilt(acceleration)was periodically modulated as above.For its analysis we have used the approximate expression forΦ(t)obtained in[13], which yields the reservoir spectrum G(ω+ωa)(Fig.2–inset),with one maximum atω∼ωg,¯hωg being the lattice band gap.The decay probability P(t),calculated in Fig.2(curves1-4)for parameters similar to[6],com-pletely coincides with that obtained for ideal impulsive measurements at intervalsτ1[2]and demonstrates either the QZE(curve2)or the AZE(curve3)behavior.The universal Eq.(7),which is a result of unitary analysis,is valid also whenǫ(t)is a stationary random process.If such a process is characterized by the corre-lation timeν−1,one can use a master equation to show that,for t≫ν−1,we have P(t)≈e−Rt,where the decay rate(provided that R≪ν)still has the general form(7), but withF t(ω)→F(ω)=π−1ǫ−2c Re ∞0|ǫ(t)|2,where the overbar denotes ensemble averaging.Expression(7)with the substitution(12)is completely analogous to the universal formula describing measurement effects on quantum evolution in[2].This analogy between unitary and measurement effects stems from the ability to emulate projective measurements bythe dephasing of the level evolution caused by classical random fields [2,5].Coupling time0.30.40.50.60.70.80.91P(µs)FIG.2.Tunneling of sodium atoms in optical lattices perturbed by AM scheme:the decay probability P (t )as a function of the total coupling time.Curves 1,4–decay with-out modulation.Curve 2–QZE (decay slowdown compared to curve 1)for τ1=0.8µs,τ0=50.8µs.Curve 3–AZE (de-cay speedup compared to curve 4)for τ1=2µs,τ0=52µs.Inset:The coupling spectrum G (ω+ωa )and the scaled mod-ulation function T −2F 4τ0(ω)for the conditions of curve 2.Here T =ωg d/(πa ),where a =15km/s 2is the lattice accel-eration and d =295nm is the lattice period.ωg =91kHz,ωg T =2.05(for curves 1,2,5);ωg =116kHz,ωg T =3.32(for curves 3,4).There may,however,be a notable difference between projections and random-field dephasing.Projective mea-surements at an effective rate ν,whether impulsive or continuous,usually result in a broadened (to a width ν)modulation function F (ω),without a shift of its cen-ter of gravity,∆= dωωF (ω)≈0[2,4].This fea-ture was shown [2]to be responsible for either the stan-dard QZE scaling,R ∼1/ν,or the AZE scaling.In contrast,a weak and broadband chaotic field such that |χ|I is the mean intensity,νB is the band-width,and χis the effective polarizability,would give rise to a Lorentzian dephasing function F (ω)in (12)with a substantial shift ∆=χI 2/νB ≪|∆|.We have presented here a general theory of dy-namically modulated quantum decay,which offers new insights into the possibilities of controlling its non-Markovian dynamics by off-resonant electromagnetic fields.Its unified form (6),(7)encompasses,as special cases,all the modulation schemes of current interest,sat-isfying the factorization condition [cf.Eq.(5)][6,7,14].Whereas its limit (12)may imitate measurement effects(the QZE and AZE),the modulation or spectral-shift pa-rameters allow us to “engineer”(suppress or enhance)more effectively the decay into a given reservoir.Thus,measurements are shown to have no advantage as a means of either suppressing or enhancing decay compared to APM.Moreover,the coherent nature of APM makes it much more appropriate than measurements for decoher-ence suppression in quantum information applications,which require reversible transformations of quantum su-perposed states.This work has been supported by EU (ATESIT Net-work),the US-Israel BSF,and the Ministry of Absorption (A.K.).。