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二维光子晶体三角晶格滤波器
曹悦;荣宪伟
【期刊名称】《黑龙江科技信息》
【年(卷),期】2016(000)009
【摘要】提出一种特殊结构的滤波器(在完整的二维光子晶体中移除相应的介质柱构成三角微腔的特殊结构).运用时域有限差分法(FDTD)对该三角结构的滤波特性进行数值模拟,模拟的情况分为两部分,一部分是对不同的波长进行滤波实验模拟,另一部分是对不同的介质柱半径进行实验模拟.分别模拟介质柱的半径为
0.1R,0.3R,0.6R.在不同的输入波长和不同的介质柱半径下,滤波器的滤波情况差别很大.计算结果表明:三角微腔滤波器对波长在2.35μm的光波透射率最高,其他波长的光波被耦合吸收,并且滤波器的滤波效果随介质柱半径的不同而变化,介质柱半径在r=0.3R时,滤波效果为最佳.
【总页数】2页(P95-96)
【作者】曹悦;荣宪伟
【作者单位】哈尔滨师范大学,黑龙江哈尔滨150046;哈尔滨师范大学,黑龙江哈尔滨150046
【正文语种】中文
【相关文献】
1.二维光子晶体三角晶格滤波器 [J], 曹悦;荣宪伟
2.三角晶格二维光子晶体带隙结构数值研究 [J], 刘丽丽;徐健良;汤炳书
3.太赫兹波段三角晶格二维光子晶体的传输特性 [J], 梁兰菊
4.柱体截面不同三角晶格二维光子晶体完全带隙的研究 [J], 廖兴展;林少光;张桂春
5.二维光子晶体三角晶格光控开关的设计 [J], 张丽聪
因版权原因，仅展示原文概要，查看原文内容请购买。
光谱灵敏度函数-回复光谱灵敏度函数是一种用来描述人眼对不同波长的光的敏感程度的函数，也被称为视觉感受函数或者眼光谱敏度。
通过测量不同波长的光对人眼的视觉反应，我们可以得到一个光谱灵敏度函数曲线，该曲线显示了在整个可见光谱范围内，人眼对不同波长的光的感知强度的变化。
光谱灵敏度函数的概念最早由德国心理学家和物理学家海顿（Hecht）和维尔斯坦（Waldstein）于1930年提出。
他们通过实验测量了在黑暗环境下人眼对不同波长的单色光的感知强度，得出了一条关于光谱灵敏度的曲线。
这个光谱灵敏度函数曲线的形状与光的波长有关，通常情况下，人眼对中等波长的绿色光的感知最为敏感，而对较短波长的紫色光和较长波长的红色光的感知较弱。
这就是为什么我们通常认为绿色是最亮的颜色，而红色和紫色看起来相对较暗。
光谱灵敏度函数的数学表示通常采用一系列的中心波长（λ）和相应的灵敏度值（S(λ)）来描述。
其中，中心波长表示光谱中最强的辐射波长，通常以纳米（nm）为单位，而灵敏度值表示人眼对该波长的相对感知强度。
光谱灵敏度函数在很多应用中都起着重要的作用。
例如，在彩色显示技术中，我们需要了解人眼对不同颜色的敏感度，以便正确地调整显示器的色彩输出。
在光谱分析领域，了解光谱灵敏度函数可以帮助我们准确地测量不同波长的光的强度。
除了人眼的光谱灵敏度函数外，还有一些其他物种的光谱灵敏度函数也被广泛研究。
例如，昆虫的光谱灵敏度函数通常与人眼有所不同，他们对紫外线波长的光有更高的感知强度。
这就是为什么某些花朵的颜色在人眼中看起来是黄色或白色，但对于昆虫来说，它们可能是具有强烈吸引力的紫色。
为了获得准确的光谱灵敏度函数曲线，研究人员使用一种特殊的工具称为分光辐射计来测量光的辐射强度。
然后，他们通过调整不同波长的单色滤光片，逐一测量人眼对不同波长的光的感知强度。
最终，通过这些数据点，他们可以绘制出光谱灵敏度函数曲线。
总的来说，光谱灵敏度函数是用于描述人眼对不同波长的光的感知强度的函数。
Bond-valence理论体系的提出和发展及Valence-matching principle的应用1、Bond-valence理论体系的提出和发展Bond-valence理论源于20世纪20年代离子晶体结构的Pauling电价规则,至今已发展成为现代结构化学一个重要内容,广泛应用于化学、物理学、晶体学、材料科学以至分子生物学领域。
1929年，美国化学家Pauling为描述无机化合物的结构引入了一种化学上直观的视角。
在这篇开创性论文中，他提出了五个描述复杂离子晶体结构的规则：I.配位多面体规则，其内容是：“在离子晶体中，在正离子周围形成一个负离子多面体，正负离子之间的距离取决于离子半径之和，正离子的配位数取决于离子半径比”。
第一规则实际上是对晶体结构的直观描述，如NaCl晶体是由[NaCl6]八面体以共棱方式连接而成。
II.电价规则指出：“在一个稳定的离子晶体结构中，每一个负离子电荷数等于或近似等于相邻正离子分配给这个负离子的静电键强度的总和，其偏差≤1/4价”。
静电键强度S=正离子数Ｚ＋/正离子配位数n ，则负离子电荷数Ｚ＝∑Si=∑(Zi+/ni)。
III.多面体共顶、共棱、共面规则，其内容是：“在一个配位结构中，共用棱，特别是共用面的存在会降低这个结构的稳定性。
其中高电价，低配位的正离子的这种效应更为明显”。
IV.不同配位多面体连接规则，其内容是：“若晶体结构中含有一种以上的正离子，则高电价、低配位的多面体之间有尽可能彼此互不连接的趋势”。
V.节约规则，其内容是：“在同一晶体中，组成不同的结构基元的数目趋向于最少”。
电价规则是Pauling五项规则的核心，其物理基础在于：如在结构中正电位较高的位置安放电价较高的负离子是，结构会趋于稳定，而某一正离子至该负离子的静电键的强度正是有关正离子在该处所引起的正电位的量度。
显然，这是一个既有其物理基础，又带有一定“经验”色彩的方法。
它突出了离子化学键的主要特征。
超声造影剂声学特性的优化设计与实验测定1宗瑜瑾，万明习，王素品，陈红西安交通大学生物医学信息工程教育部重点实验室，生命科学与技术学院，西安(710049)E-mail：mxwan@摘要：本文基于超声造影剂微泡在声场中的理论振动模型，建立了用于对超声造影剂的声学特性进行优化设计与分析的计算机辅助设计系统。
利用该系统，从理论上计算和估计不同的微泡半径、声压等参数对微泡的基波和二次谐波的影响，以得到获得最佳二次谐波特性的声学条件。
并在此基础上，对优化条件下超声造影剂的声学特性进行了体外声学实验测定。
实验结果表明，该优化设计系统的计算结果在一定范围内能够与实验结果较好地吻合，可从理论上对造影剂的制备和应用进行指导。
关键词：超声造影剂，声压，基波，二次谐波1．前言与其它成像模式中造影剂的作用类似，超声造影剂(Ultrasound contrast agent, UCA)是一类能够显著增强医学超声成像信号的诊断试剂。
由于超声造影剂与周围组织的声阻抗差高、共振散射强，可显著增强在组织背景下血液流动中UCA的散射信号，所以在微血管血流灌注成像方面具有很大的潜力[1-5]。
目前，超声造影剂已从当初的自由气泡发展成为蛋白质、表面活性剂、脂类或聚合物等包膜并包裹高分子量难溶气体的微泡。
包膜的存在增加了微泡的“寿命”，使微泡内的气体不容易溶解、扩散到周围的血液中，提高了微泡的稳定性。
但是包膜的存在又影响了微泡在声场中的振动，使得微泡在声场中的行为变得更加复杂[6-9]。
为了能够更好地了解超声造影剂在声场作用下的振动，找到其用于基波增强、谐波成像等不同成像模式时的最佳工作条件。
本文基于单个超声造影剂在声场中振动的理论模型，建立了超声造影剂声学特性的优化设计分析系统，用于微泡声学特性的计算机辅助设计和分析。
从理论上计算不同声学参数的条件下超声造影剂的半径振动曲线和散射回波，并利用体外声学测试系统测定了自制的JD-95型超声造影剂在不同优化条件下的声学特性。
高速平板边界层中定常条带的前缘感受性
刘洋;赵磊
【期刊名称】《空气动力学学报》
【年(卷),期】2024(42)4
【摘要】来流湍流度较高时,自由流涡波可在边界层内激发流向条带结构,并引起边界层的旁路(bypass)转捩。
本文采用调和线性化Navier-Stokes方程(harmonic linearized Navier-Stokes,HLNS)方法模拟平板边界层条带对自由流涡波的前缘感受性,并通过直接数值模拟验证了HLNS方法的可靠性。
针对马赫数4.8的高速平
板边界层,分析了零频涡波激发定常条带的前缘感受性过程及定常条带的演化规律。
研究结果表明,边界层外的自由流涡扰动对边界层条带的发展存在持续的激励作用;
对于固定展向波数的自由流涡波,法向波数为0时激发的条带幅值最大;自由流涡波的法向波数在小于临界角度时仅影响条带的幅值,而不影响条带扰动的形函数剖面。
随着当地雷诺数的增加,条带的幅值演化和形函数剖面呈现出很好的相似性;当地无
量纲展向波数β=0.18时,归一化幅值最大。
【总页数】14页(P14-26)
【作者】刘洋;赵磊
【作者单位】天津大学力学系;天津市现代工程力学重点实验室
【正文语种】中文
【中图分类】V211;V411;O357.4
【相关文献】
1.PIV测量非定常自由来流中的三角翼前缘涡
2.前缘曲率变化对平板边界层感受性问题的影响
3.无限薄平板边界层前缘感受性过程的数值研究∗
4.前缘曲率对三维边界层内被激发出非定常横流模态的影响研究
5.高超声速平板边界层/圆柱粗糙元非定常干扰
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半导体量子点内弹性应变能的研究(英文)
杨红波;俞重远;刘玉敏;黄永箴
【期刊名称】《人工晶体学报》
【年(卷),期】2004(33)4
【摘要】本文用有限元分析软件ANSTS 6 .0计算了半导体量子点内的弹性应变和弹性应变能 ,通过对金塔形、台形和圆顶形量子点内总弹性应变能的计算和总能量的比较 ,得到了在热平衡条件下金字塔形量子点是最稳定的结构。
【总页数】4页(P531-534)
【关键词】有限元分析软件;半导体量子点;弹性应变;弹性应变能
【作者】杨红波;俞重远;刘玉敏;黄永箴
【作者单位】北京邮电大学理学院;中国科学院半导体研究所,集成光电子学国家重点联合实验室
【正文语种】中文
【中图分类】O472
【相关文献】
1.异质外延自组织量子点弹性应变场分布的研究 [J], 刘玉敏;俞重远;杨红波;黄永箴
2.剩余应变对半导体量子点边带能影响的数值分析 [J], 杨红波;俞重远
3.Ge/Si半导体量子点的应变分布与平衡形态 [J], 蔡承宇;周旺民
4.有限元法分析透镜形自组织生长量子点的弹性应变场分布(英文) [J], 刘玉敏;俞
重远;杨红波;黄永箴
5.1.55μm张应变InGaAsP/InGaAsP量子阱偏振不灵敏半导体光放大器的优化设计(英文) [J], 邱伟彬;何国敏;董杰;王圩
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NMR中常用的英文缩写和中文名称汪茂田译注APTAttached Proton Test 质子连接实验ASISAromatic Solvent Induced Shift 芳香溶剂诱导位移BBDRBroad Band Double Resonance 宽带双共振BIRDBilinear Rotation Decoupling 双线性旋转去偶（脉冲）COLOCCorrelated Spectroscopy for Long Range Coupling 远程偶合相关谱COSY( Homonuclear chemical shift ) COrrelation SpectroscopY （同核化学位移）相关谱CPCross Polarization 交叉极化CP/MASCross Polarization / Magic Angle Spinning 交叉极化魔角自旋CSAChemical Shift Anisotropy 化学位移各向异性CSCMChemical Shift Correlation Map 化学位移相关图CWcontinuous wave 连续波DDDipole-Dipole 偶极-偶极DECSYDouble-quantum Echo Correlated Spectroscopy 双量子回波相关谱DEPTDistortionless Enhancement by Polarization Transfer 无畸变极化转移增强2DFTStwo Dimensional FT Spectroscopy 二维傅立叶变换谱DNMRDynamic NMR 动态NMRDNPDynamic Nuclear Polarization 动态核极化DQ(C)Double Quantum (Coherence) 双量子（相干）DQDDigital Quadrature Detection 数字正交检测DQFDouble Quantum Filter 双量子滤波DQF-COSYDouble Quantum Filtered COSY 双量子滤波COSYDRDSDouble Resonance Difference Spectroscopy 双共振差谱EXSYExchange Spectroscopy 交换谱FFTFast Fourier Transformation 快速傅立叶变换FIDFree Induction Decay 自由诱导衰减H,C-COSY1H,13C chemical-shift COrrelation SpectroscopY 1H,13C化学位移相关谱H,X-COSY1H,X-nucleus chemical-shift COrrelation SpectroscopY 1H,X-核化学位移相关谱HETCORHeteronuclear Correlation Spectroscopy 异核相关谱HMBCHeteronuclear Multiple-Bond Correlation 异核多键相关HMQCHeteronuclear Multiple Quantum Coherence异核多量子相干HOESYHeteronuclear Overhauser Effect Spectroscopy 异核Overhause效应谱HOHAHAHomonuclear Hartmann-Hahn spectroscopy 同核Hartmann-Hahn谱HRHigh Resolution 高分辨HSQCHeteronuclear Single Quantum Coherence 异核单量子相干INADEQUATEIncredible Natural Abundance Double Quantum Transfer Experiment 稀核双量子转移实验（简称双量子实验，或双量子谱）INDORInternuclear Double Resonance 核间双共振INEPTInsensitive Nuclei Enhanced by Polarization 非灵敏核极化转移增强INVERSEH,X correlation via 1H detection 检测1H的H,X核相关IRInversion-Recovery 反（翻）转回复JRESJ-resolved spectroscopy J-分解谱LISLanthanide (chemical shift reagent ) Induced Shift 镧系（化学位移试剂）诱导位移LSRLanthanide Shift Reagent 镧系位移试剂MASMagic-Angle Spinning 魔角自旋MQ(C)Multiple-Quantum ( Coherence ) 多量子（相干）MQFMultiple-Quantum Filter 多量子滤波MQMASMultiple-Quantum Magic-Angle Spinning 多量子魔角自旋MQSMulti Quantum Spectroscopy 多量子谱NMRNuclear Magnetic Resonance 核磁共振NOENuclear Overhauser Effect 核Overhauser效应（NOE）NOESYNuclear Overhauser Effect Spectroscopy 二维NOE谱NQRNuclear Quadrupole Resonance 核四极共振PFGPulsed Gradient Field 脉冲梯度场PGSEPulsed Gradient Spin Echo 脉冲梯度自旋回波PRFTPartially Relaxed Fourier Transform 部分弛豫傅立叶变换PSDPhase-sensitive Detection 相敏检测PWPulse Width 脉宽RCTRelayed Coherence Transfer 接力相干转移RECSYMultistep Relayed Coherence Spectroscopy 多步接力相干谱REDORRotational Echo Double Resonance 旋转回波双共振RELAYRelayed Correlation Spectroscopy 接力相关谱RFRadio Frequency 射频ROESYRotating Frame Overhauser Effect Spectroscopy 旋转坐标系NOE谱ROTOROESY-TOCSY Relay ROESY-TOCSY 接力谱SCScalar Coupling 标量偶合SDDSSpin Decoupling Difference Spectroscopy 自旋去偶差谱SESpin Echo 自旋回波SECSYSpin-Echo Correlated Spectroscopy自旋回波相关谱SEDORSpin Echo Double Resonance 自旋回波双共振SEFTSpin-Echo Fourier Transform Spectroscopy (with J modulation) （J-调制）自旋回波傅立叶变换谱SELINCORSelective Inverse Correlation 选择性反相关SELINQUATESelective INADEQUATE 选择性双量子（实验）SFORDSingle Frequency Off-Resonance Decoupling 单频偏共振去偶SNR or S/NSignal-to-noise Ratio 信/ 燥比SQFSingle-Quantum Filter 单量子滤波SRSaturation-Recovery 饱和恢复TCFTime Correlation Function 时间相关涵数TOCSYTotal Correlation Spectroscopy 全（总）相关谱TOROTOCSY-ROESY Relay TOCSY-ROESY接力TQFTriple-Quantum Filter 三量子滤波WALTZ-16A broadband decoupling sequence 宽带去偶序列WATERGATEWater suppression pulse sequence 水峰压制脉冲序列WEFTWater Eliminated Fourier Transform 水峰消除傅立叶变换ZQ(C)Zero-Quantum (Coherence) 零量子相干ZQFZero-Quantum Filter 零量子滤波T1Longitudinal (spin-lattice) relaxation time for MZ 纵向（自旋-晶格）弛豫时间T2Transverse (spin-spin) relaxation time for Mxy 横向（自旋-自旋）弛豫时间tmmixing time 混合时间τ crotational correlation time 旋转相关时间。
a rX iv:c ond-ma t/971223v1[c ond-m at.str-el]18D ec1997EUROPHYSICS LETTERS Europhys.Lett.,(),pp.()Orbital polarization in LiVO 2and NaTiO 2S.Yu.Ezhov 1,V.I.Anisimov 1,H.F.Pen 2,D.I.Khomskii 2,G.A.Sawatzky 21Institute of Metal Physics,GSP-170,Ekaterinburg,Russia 2Laboratory of Applied and Solid State Physics,Materials Science Centre,Univer-sity of Groningen,Nijenborgh 4,9747AG Groningen,The Netherlands (received ;accepted )PACS.71.15Mb –Density functional theory,local density approximation.PACS.71.27+a –Strongly correlated electron systems;heavy fermions.PACS.71.20−b –Electron density of states and band structure of crystalline solids.Abstract.–We present a band structure study of orbital polarization and ordering in the two-dimensional triangular lattice transition metal compounds LiVO 2and NaTiO 2.It is found that while in NaTiO 2the degeneracy of t 2g orbitals is lifted due to the trigonal symmetry of the crystal and the strong on cite Coulomb interaction,in LiVO 2orbital degeneracy remains and orbital ordering corresponding to the trimerization of the two-dimensional lattice develops.It is well known that transition metal compounds with orbital degeneracy will in some way restructure to remove that orbital degeneracy in the ground state.Well known is the example of a two-fold orbitally degenerate case of divalent Cu in octahedral symmetry with one hole in a e g -like orbital.A similar case is trivalent Mn in O h symmetry as in the now well known collossal magnetoresistance materials.In these so called strong Jan Teller systems local lattice distortions determine the type of orbital ordering.It is also well established that the relative spatial orientation of occupied orbitals on neighboring ions determines not only the magnitude but also the sign of the exchange interactions governing the magnetic structure of the system [1].In the early 3d transition metal compounds only the t 2g orbitals are occupied leaving us with three-fold degeneracy in the cases of Ti 3+and V 3+with one and two 3d electrons respectively assuming also O h symmetry.In contrast to the e g orbitals thebonding to the neighboring O 2p orbitals is much weaker,bandwidths are much smaller and therefore the removal of the orbital degeneracy may be more subtle.It has for example recently been suggested that the orbital degeneracy in LiVO 2can be lifted by a particular kind of orbital ordering driven by the nearest neighbor exchange interactions [2].The orbital ordering proposed there is one which simultaniously removes the frustration in the spin Hamiltonian of this triangular two-dimensional lattice and results in a non magnetic singlet ground state.Another much discussed two-dimensional triangular lattice spin system is NaTiO2with spin 1trigonal,and in that case the t2g level is split into a nondegenerate A1g and double degenerateS.E gbethe√2)(√4Fig.3.upperwithlocalpointsoneband90◦,sotheand a more delicate quantitative analysis is needed to clarify this problem.In the right panel offig.2the partial DOS for decomposition of the t2g band into orbitals of the A1g and E g symmetry are presented.One can see that the situation can not be described in the simple terms of A1g-E g”splitting”:both curves have the same width and they are approximately in the same energy region.We can estimate the actual splitting of the A1g and E g levels by calculating the values of the centres of gravity of these bands.In the case of NaTiO2with one d electron the center of gravity of the A1g band is0.1eV lower than that of the E g band.As a result the occupied part of t2g band has slightly more A1g character than E g,and the occupancy of orbitals are.25and.20per spin-orbital for A1g and for each E g correspondingly.This means that the degeneracy of the t2g orbitals is essentially lifted but the splitting is still much less than the band widths.This small splitting is non theS.EZHOV et al.:ORBITAL POLARIZATION IN LiVO2AND NaTiO25Fig.4.–The t2g holes from LDA+U calculations for LiVO2.Only V atoms for one triangle in a hexagonal plane are drawn.The view is from the point directly above V-triangleless important since as we will see below if we turn on the d-d Coulomb interaction in LDA+U the A1g band will be occupied and the E g unocupied now with a splitting mainly due to U. However the choice as to which band is occupied and which one not is dictated by the small crystalfield splitting.The above result would also indicate that the A1g-E g local excitation energy would be only0.1eV or so and would contribute to charge conserving excitonic-like excitations.In this LDA+U calculation the d-d Coulomb interaction was found to be3.6eV (taking into account the screening of t2g electrons by e g electrons[12])which is much larger than the t2g band width and leads to the localization of a single d electron in the A1g orbital.The LDA+U calculations were carried out for both antiferromagnetic and ferromagnetic cases.For the AFM case we choose the simplest magnetic order with four nearest neighbors out of the six in the basal plane having anti-parallel spin orientation and other two parallel. Independent of the spin ordering a single d electron in the t2g shell of the Ti ion turned out to be localized in the A1g orbital.The occupation numbers for the majority spin are0.9 for A1g and0.1for E g for both FM and AFM cases.The Ti(3d)projected density-of-states obtained from LDA+U calculations is shown infig.3(a).So we can say from thefig.3(a)that the LDA+U solution for NaTiO2is almost fully orbitally polarized.One can see from eq.1 that the A1g orbital(d3z2−r2infig.3(a))is symmetric in the hexagonal Ti-Ti plane and the occupation of this orbital leads to the isotropic exchange.This indicates that NaTiO2would still behave like a frustrated spin system.In the case of LiVO2the centre of gravity of the A1g band is only0.025eV lower then the centre of gravity of the E g band,and the resulting occupancies are0.37and0.36for A1g and for each E g-orbitals correspondingly.In this situation orbital degeneracy is not lifted,since we now have two electrons one in a A1g and one in a E g orbital,because the Hunds rule exchange6EUROPHYSICS LETTERS strongly favours the high spin state.As a result the appearance of some kind of orbital order can be expected.In[2,13,14]the formation of local spin singlets on trimers containing V-atom triangles was suggested as the model explaining the low-temperature nonmagnetic behavior of LiVO2.Those spin singlets were stabilized by a specific orbital order[2].The LDA+U method is based on a mean-field approximation and can not fully reproduce the essentially many-electron singlet wave function,especially the correct energy difference of singlet-triplet configurations.However a single Slater determinant trial wave function can still describe the basic relationship between spin and orbital degrees of freedom.To imitate trimer spin singlets we performed LDA+U calculations with spin-order of the type”up-down-zero”on every triangle(closed circles on thefig.1).The self-consistent calculations resulted in the orbital order of the same type as proposed in[2]from model calculations[fig.3(b)]:on every V atom the occupied orbitals are xz and yz if in a local coordinate system z axis is directed towards the oxygen atom sitting just above the center of V-triangle,and x and y axes are directed towards other oxygens of an octahedron(fig.1).We should also mention the fact that the LDA+U calculations give the correct semiconducting state for LiVO2[fig.3(b)]instead of a metallic state from”normal”LDA(left panel offig.2).Infig.4the angular distribution of the t2g hole is presented as was obtained from the LDA+U calculations.It indicates the same orbital order proposed in[2](fig.1(a)in[2]):xz and yz orbitals are occupied,the t2g hole is in xy orbital in a local coordinate system of every V atom.Both LiVO2and NaTiO2were regarded as candidates for realization of Anderson’s”res-onating valence bond”systems with a quantum liquid of randomly distributed spin singlet pairs.Our results show that while in LiVO2more complicated trimer spin singlets with corresponding orbital order are formed,no orbital order due to the crystalfield lifting of the orbital degeneracy is present in NaTiO2,and its magnetic properties are most probably explained by a nondegenerate model,so that it is indeed a good candidate for Anderson’s RVB state.What then is the nature of the structural phase transition observed in NaTiO2at T c=250,remains an open question.Summarizing,we have shown that the degeneracy of the t2g-orbitals in NaTiO2is lifted because of the trigonal symmetry of the crystal and the large d-d Coulomb interaction and no orbital ordering occurs.In LiVO2orbital degeneracy remains in spite of the same trigonal distortion as in NaTiO2,and in effect the orbital ordering consistent with the trimerization of the two-dimensional lattice takes place.***We thank Dr.S.J.Clarke for providing us with the detailed data of the NaTiO2crystal structure prior to publication.This investigation was supported by the Russian Foundation for Fundamental Investigations(RFFI grant9602-16167)and by the Netherlands Organization for Fundamental Research on Matter(FOM),withfinancial support by the Netherlands Organization for the advance of Pure Science(NWO).REFERENCES[1]K.I.Kugel and D.I.Khomskii,p.,25231(1982).[2]H.F.Pen,J.van den Brink,D.I.Khomskii,G.A.Sawatzky,Phys.Rev.Lett.,781323(1997).[3]P.W.Anderson,Science,2351196(1987);P.W.Anderson,Mater.Res.Bull.,8153(1973).[4]P.F.Bongers,Ph.D.thesis,(University of Leiden)1957.[5]K.Kobayashi,K.Kosuge,S.Kashi,Mater.Res.Bull.,495(1969);L.P.Cardoso,D.E.Cox,T.A.Hewston,B.L.Chamberland,J.Solid State Chem.,72234(1988).S.EZHOV et al.:ORBITAL POLARIZATION IN LiVO2AND NaTiO27[6]K.Terakura,T.Oguchi,A.R.Williams,J.K¨u bler,Phys.Rev.B,304734(1984).[7]Andersen O.K.,Phys.Rev.B,123060(1975).[8]P.Hoenberg,W.Kohn,Phys.Rev.,136B864(1964);W.Kohn,L.J.Sham,Phys.Rev.,140A1133(1965).[9]V.I.Anisimov,J.Zaanen,Andersen O.K.,Phys.Rev.B,44943(1991);V.I.Anisimov,F.Aryasetiawan,A.I.Lichtenstein,J.Phys.:Condens.Matter,9767(1997).[10]Katsushiro Imai,Hiroshi Sawa,Masayoshi Koike,Masashi Hasegawa,Humihiko Takei,J.Solid State Chem.,114184(1995).[11]S.J.Clarke,A.C.Duggan,A.J.Fowkes,A.Harrison,R.M.Ibberson,M.J.Rosseinsky,m.,(1996)409;S.J.Clarke,(private communication).[12]V.I.Anisimov,O.Gunnarsson,Phys.Rev.B,437570(1991);W.E.Pickett,S.E.Erwin,E.C.Ethridge,(Preprint No.condens-matter/9611225).[13]G.B.Goodenough,Magnetism and the Chemical bond,(Interscience Publishers,N.Y.)1963p.269.[14]G.B.Goodenough,G.Dutta,and A.Manthiram,Phys.Rev.B.,4310170(1991).。
实例1VASP算稀土永磁材料的磁学性能用哪种算法和赝势比较好？用VASP计算稀土永磁材料（比如Sm-Co）的磁学性能用哪种算法和赝势比较好啊？LDA GGA LSDA+U?PBE PW91?PBE是比较好的交换关联能，但是对于磁性，最后加上U结果可能会好点。
但是U的确定需要从文献和其他软件得到我算的磁性没有f电子，这是为什么呢？是赝势的问题还是将f电子限制在芯内了？f电子的确是很深的，一般很难和其他原子的电子相互作用，这也是La系和Ac的元素的化学表现很相似的原因那么怎样才能使磁性计算出现f电子呢？确实让人纠结啊！请问使用PBEsol+U进行优化和性质计算,如何设置INCAR？在vasp5.2手册上找不到PBEsol+U的说明，只有LSDA+U的PBE是GGA类的交换关联能，LSDA的设置是可以同样用于GGA的实例2vasp计算中sigmma值稀土金属怎么取vasp计算中sigmma值稀土金属怎么取啊？计算出来老感觉不对。
取不同的sigma测试，然后，计算结果中取能量的哪一行，sigma-->0跟不趋近0的时候的比较，差别满足你的精度需求就是实例3关于VASP计算用不同赝势产生的能量差异！为啥同一个结构，用不同的赝势文件POTCAR，如PAW_PBE赝势和用US赝势来计算，为啥能量不一样？连初始第一步的能量的差别就很大啊？本人理论知识很浅，各位大侠能说说其中原理吗？这不只是精度的问题，因为能量就不在一个层次上！两套赝势的能量没有可比性.Generally the PAW potentials are more accurate than the ultra-soft pseudopotentials. There are two reasons forthis: first, the radial cutoffs (core radii) are smaller than the radii used for the USpseudopotentials, and second thePAW potentials reconstruct the exact valence wave function with all nodes in the core region.能量绝对值没有任何意义的，不同赝势能量参考态不一样，只有能量之差才有意义。
基于单个槽波导微环谐振器法诺共振的折射率传感
李鑫雨;徐强;孙士博;孔梅;徐亚萌
【期刊名称】《半导体光电》
【年(卷),期】2024(45)1
【摘要】法诺线型的不对称和窄线宽特性有利于实现具有高传感灵敏度和低可探
测极限的折射率传感。
采用三维时域有限差分法,基于槽波导设计了微环谐振器和
法布里-珀罗腔的耦合结构,实现了法诺线型谱线,并利用其提升折射率传感器的性能。
不同于已报道的多微环级联等复杂结构,基于单个槽波导微环实现了法诺线型谱线,
并在波长探测传感方案下得到传感灵敏度为500 nm/RIU,可探测极限为
4.00×10^(-5) RIU;在强度探测传感方案下,传感灵敏度为7.24×10~4 dB/RIU,可
探测极限为5.52×10^(-6) RIU。
【总页数】6页(P56-61)
【作者】李鑫雨;徐强;孙士博;孔梅;徐亚萌
【作者单位】长春理工大学物理学院光电信息科学与技术系
【正文语种】中文
【中图分类】TN256
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多激励模式下的电容层析传感器优化设计作者：杨博韬，王莉莉，陈德运，陈峰来源：《哈尔滨理工大学学报》2022年第01期摘要：针对电容层析成像（ECT）系统中传感器采集信号微弱，边缘化效应严重，介电常数变化不明显等问题，提出了一种基于多激励模式下的ECT传感器优化设计方案，该方案在优化了传感器物理参数的同时采用相邻双电极激励模式进行检测，增加了敏感场强度，在一次测量过程中可以获得更多的电容值，有效增加了传感器采集信号数量与采集精度。
实验结果表明，优化后的ECT传感器能有效提高激励信号强度，减弱边缘化效应，改善传感器内部灵敏度矩阵，提高采集信号精度，图像重建质量明显提高。
关键词：电容层析成像;传感器优化设计;多激励模式;图像重建DOI：10.15938/j.jhust.2022.01.007中图分类号： TP216 文献标志码： A 文章编号： 1007-2683（2022）01-0047-08Optimal Design of Electrical Capacitance TomographySensor Based on Multiple Excitation ModesYANG Botao，WANG Lili，CHEN Deyun，CHEN Feng（School of Computer Seience and Technology， Harbin University of Science and Technology， Harbin 150080， China）Abstract：Aiming at the problems of weak sensor acquisition signal， serious marginal effect，and insignificant change in dielectric constant in the electrical capacitance tomography （ECT）system， an optimized design scheme of ECT sensor based on multiple excitation modes is proposed. This scheme optimizes the physical parameters of the sensor and adopts adjacent double the electrode excitation mode is used for detection， which increases the intensity of the sensitive field， and obtains more capacitance values in a measurement process， which effectively increases the number of signals collected by the sensor and the acquisition accuracy. The experimental results show that the ECT sensor with multiple excitation modes can effectively increase the excitation signal strength，reduce the marginal effect， improve the internal sensitivity matrix of the sensor， increase the accuracy of the acquisition signal， and significantly improve the image reconstruction quality.Keywords：electrical capacitance tomography; sensor optimization design; multiple excitation modes; image reconstruction0引言電容层析成像（electrical capacitance tomography，简记ECT）技术[1]，是近年来发展起来的一种基于电容感应原理的新型流动层析成像技术，属于过程层析成像（process tomography，简记PT）技术的一种，是以医学X射线断层扫描技术（computed tomography，简记CT）为基础发展起来的一种过程参数实时在线检测技术，可对封闭管道或容器内的导电流体进行可视化测量[2]，利用交变激励电场从多个角度对封闭空间内部进行探测，物场中的导电流体在外加电场的激励下产生感应电荷，对主电场产生调制作用。
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铜超导温度引言超导材料是一类在低温下具有零电阻和完全磁场排斥性质的材料。
在过去的几十年里，科学家们一直在寻找能够在更高温度下实现超导的材料。
铜是一种常见的金属，在室温下具有良好的导电性能。
本文将探讨铜的超导温度及其相关性质。
铜的超导性质超导是指材料在低温下电阻突然消失的现象。
铜在常规条件下不表现出超导性质，因为其临界温度（超导转变温度）远低于室温。
然而，通过改变铜的结构或合金化，可以提高其超导温度。
铜的结构改变铜的超导温度可以通过改变其晶体结构来提高。
例如，通过施加高压，可以使铜的晶体结构发生变化，从而提高其超导温度。
此外，通过掺杂其他元素，如氧、硼等，也可以改变铜的晶体结构，从而提高其超导温度。
铜的合金化除了结构改变外，合金化也是提高铜超导温度的常用方法。
通过将铜与其他金属元素合金化，可以改变其晶格结构和电子结构，从而提高其超导温度。
例如，铜和钴的合金化可以使超导温度从几十摄氏度提高到几百摄氏度。
铜的超导温度提高的挑战尽管已经取得了一些进展，但提高铜的超导温度仍然面临着一些挑战。
首先，铜的超导温度远低于室温，因此需要极低的温度条件才能实现超导。
其次，铜的超导性质与其晶体结构和电子结构密切相关，因此需要深入理解和控制这些性质才能提高其超导温度。
结论虽然铜的超导温度相对较低，但通过结构改变和合金化等方法，科学家们已经取得了一些进展，使其超导温度得到提高。
进一步的研究和探索将有助于我们更好地理解铜的超导性质，并为实现更高超导温度的材料提供指导。
参考文献1.John D. Lee, “High-temperature superconductivity in copper-basedcompounds”, Reports on Progress in Physics, 1993.2.P. W. Anderson, “The Resonating Valence Bond State in La2CuO4 andSuperconductivity”, Science, 1987.3.J. G. Bednorz and K. A. Müller, “Possible High TcSuperconductivity in the Ba-La-Cu-O System”, Zeitschrift fürPhysik B, 1986.4.T. Hasegawa, “Superconductivity in Cu-Based Compounds”, Journalof the Physical Society of Japan, 1988.。
《光电技术》专业英语词汇Absorption coefficient 吸收系数absorption region in APD APD 吸收区域Acceptance angle 接收角Acceptors in semiconductors 半导体接收器Acousto-optic modulator 声光调制active medium 活动介质Active pixel sensor 有源像素传感器active region 活动区域Air disk 艾里斑Airy rings 艾里环Aliasing 伪信号Amorphous silicon photoconversion layer 非晶硅存储型amplifiers 放大器angular radius 角半径anisotropy 各向异性Antireflection coating 抗反膜Argon-ion laser 氩离子激光器Attenuation coefficient 衰减系数Automatic gain control 自动增益控制Avalanche photodiode(APD) 雪崩二极管Avalanche 雪崩Average irradiance 平均照度bandgap diagram 带隙图Bandgap 带隙Bandwidth 带宽Beam splitter cube 立方分束器Beam 光束Bias 偏压Biaxial crystals 双轴晶体41. Birefringent 双折射Bit rate 位率Black body radiation law 黑体辐射法则Bloch wave in a crystal 晶体中布洛赫波Block access 块存取Blooming 高光溢出Boundary conditions 边界条件Bragg angle 布拉格角度Bragg diffraction condition 布拉格衍射条件Bragg diffraction 布拉格衍射Bragg wavelength 布拉格波长breakdown voltage 击穿电压Brewster angle 布鲁斯特角Brewster window 布鲁斯特窗Calcite 霰石Carrier confinement 载流子限制Centrosymmetric crystals 中心对称晶体characteristics-table 特性表格Charge coupled device 电荷耦合组件Charge handling capability 操作电荷量Chirping 啁啾Chrominance difference signal 色差信号Cladding 覆层Clamp 钳位cleaved-coupled-cavity 解理耦合腔Coefficient of index grating 指数光栅系数Coherence 连贯性Color temperature 色温Compensation doping 掺杂补偿Complementary color 补色Complementary metal oxide semi-conductor 互补金属氧化物半导体Conduction band 导带Conduction band 导带Conductivity 导电性Confining layers 限制层Conjugate image 共轭像Conversion efficiency 转换效率Correlated double sampling 相关双采样Cut-off wavelength 截止波长Dark current 暗电流Defect correction 缺陷补偿Degenerate semiconductor 简并半导体Density of states 态密度Depletion layer 耗尽层Depletion layer 耗尽层Detectivity 探测率Dielectric mirrors 介电质镜像Diffraction grating equation 衍射光栅等式Diffraction grating 衍射光栅Diffraction 衍射Diffusion current 扩散电流Diffusion current 扩散电流Diffusion flux 扩散流量Diffusion Length 扩散长度Diode equation 二极管公式Diode ideality factor 二极管理想因子Direct recombination 直接复合Discrete cosine transform 离散余弦变换Dispersion 散射Dispersive medium 散射介质distributed Bragg reflection 分布布拉格反射Distributed Bragg reflector 分布布拉格反射器distributed feedback 分布反馈Donors in semiconductors 施主离子Doppler broadened linewidth 多普勒扩展线宽Doppler effect 多普勒效应Doppler-heterostructure 多普勒同质结构Doppler shift 多普勒位移Drift current 漂移电流Drift mobility 漂移迁移率Drift Velocity 漂移速度Dynamic range 动态范围Edge enhancement 轮廓校正Effective density of states 有效态密度Effective mass 有效质量Effective pixel 有效像素efficiency of the He-Ne 氦氖效率Efficiency 效率Einstein coefficients 爱因斯坦系数Electrical bandwidth of fibers 光纤电子带宽Electromagnetic wave 电磁波Electron affinity 电子亲和势Electron potential energy in a crystal 晶体电子阱能量Electronic shutter 电子快门Electro-optic effects 光电子效应Energy band diagram 能量带宽图Energy band 能带Energy band 能量带宽energy gap 能级带隙Energy level 能级Epitaxial growth 外延生长Erbium doped fiber amplifier 掺饵光纤放大器Excess carrier distribution 过剩载流子扩散External photocurrent 外部光电流Extrinsic semiconductors 本征半导体Fabry-Perot laser amplifier 法布里-珀罗激光放大器Fabry-Perot optical resonator 法布里-珀罗光谐振器Faraday effect 法拉第效应Fermi energy 费米能级Fermi-Dirac function 费米狄拉克结fibers 光纤Field integration 场读出方式Fill factor 填充因子Fixed pattern noise 固定图形噪声Floating diffusion amplifier 浮置扩散放大器Floating gate amplifier 浮置栅极放大器Frame integration 帧读出方式Frame interline transfer CCD 帧行间转移 CCDFrame transfer CCD 帧转移 CCDFrame transfer 帧转移Free spectral range 自由谱范围Fresnel’s equations 菲涅耳方程Fresnel’s optical indicatrix 菲涅耳椭圆球Fringing field drift 边缘电场漂移Full frame CCD 全帧 CCDFull width at half maximum 半峰宽Full width at half power 半功率带宽Fundamental absorption edge 基本吸收带Gaussian beam 高斯光束Gaussian dispersion 高斯散射Gaussian pulse 高斯脉冲Glass perform 玻璃预制棒Global exposure 全面曝光Goos Haenchen phase shift Goos Haenchen 相位移Graded index rod lens 梯度折射率棒透镜Group delay 群延迟Group velocity 群参数guard ring 保护环Half-wave plate retarder 半波延迟器Helium-Neon laser 氦氖激光器Heterojunction 异质结Heterostructure 异质结构High frame rate readout mode 高速读出模式Hole 空穴129.Hologram 全息图Holography 全息照相Homojunction 同质结Horizontal CCD 水平 CCDHuygens-Fresnel principle 惠更斯-菲涅耳原理Iconoscope 光电摄像管Illuminance 照度Image lag 残像Image sensor 图像传感器Image stabilizer 手振校正Impact-ionization 碰撞电离Index matching 指数匹配Injection 注射Instantaneous irradiance 自发辐射Integrated optics 集成光路Intensity of light 光强Interlace scan 隔行扫描Interline transfer CCD 行间转移型 CCDinternal gain 内增益Intersymbol interference 符号间干扰Intrinsic concentration 本征浓度Intrinsic semiconductors 本征半导体Irradiance 辐射ISO sensitivity ISO 感光度Laser diode 激光二极管LASER 激光Lasing emission 激光发射LED 发光二极管Line transfer 线转移Lineshape function 线形结Linewidth 线宽Lithium niobate 铌酸锂Load line 负载线Loss coefficient 损耗系数Luminance signal 高度信号Luminous quantity 测光量Macrobending loss 宏弯损耗Magneto-optic effects 磁光效应Magneto-optic isolator 磁光隔离Magneto-optic modulator 磁光调制Majority carrier 多数载流子Majority carriers 多数载流子Matrix emitter 矩阵发射Maximum acceptance angle 最优接收角Maxwell’s wave equation 麦克斯维方程Mazh-Zehnder modulator Mazh-Zehnder 型调制器Microbending loss 微弯损耗Microlaser 微型激光CMOS image sensor COMS 图像传感器Minimum illumination 最低照度Minority carrier 少数载流子Minority carriers 少数载流子Modulated directional coupler 调制定向偶合器Modulation of light 光调制Monochromatic wave 单色光MOS diode MOS 二极管MOS image sensor MOS 型图像传感器multiple quantum well 多量子阱multiplication factor 倍增因子Multiplication region 倍增区Negative absolute temperature 负温度系数Net round-trip optical gain 环路净光增益Noise 噪声Non interlace 逐行扫描Noncentrosymmetric crystals 非中心对称晶体Nondegenerate semiconductors 非简并半异体Non-linear optic 非线性光学Non-thermal equilibrium 非热平衡Normalized frequency 归一化频率Normalized index difference 归一化指数差异Normalized propagation constant 归一化传播常数Normalized thickness 归一化厚度Numerical aperture 孔径Nyquist frequency 奈奎斯特频率Optic axis 光轴Optic fibers 光纤Optical activity 光活性Optical anisotropy 光各向异性Optical bandwidth 光带宽Optical cavity 光腔Optical divergence 光发散Optical fiber amplifier 光纤放大器Optical field 光场Optical gain 光增益Optical indicatrix 光随圆球Optical isolater 光隔离器Optical isotropic 光学各向同性的Optical Laser amplifiers 激光放大器Optical modulators 光调制器Optical pumping 光泵浦Optical resonator 光谐振器Optical tunneling 光学通道optical 光学的oscillation condition 振荡条件Outside vapor deposition 管外气相淀积Overflow 溢出Passive pixel sensor 无源像素传感器Passive 无源Penetration depth 渗透深度Phase change 相位改变Phase condition in lasers 激光相条件Phase matching angle 相位匹配角Phase matching 相位匹配Phase mismatch 相位失配Phase modulation 相位调制Phase modulator 相位调制器Phase of a wave 波相217.Phase velocity 相速Phonon 光子Photoconductive detector 光导探测器Photoconductive gain 光导增益Photoconductivity 光导性Photocurrent 光电流Photodetector 光探测器Photodiode 光电二极管Photodiode 光电二极管Photoelastic effect 光弹效应Photogeneration 光子再生photogeneration 光子再生Photolelctric effect 光电效应Photon amplification 光子放大Photon confinement 光子限制Photortansistor 光电三极管Photovoltaic devices 光伏器件Piezoelectric effect 压电效应Pinned photodiode 掩埋型光电二极管Pixel signal interpolating 插值处理Planck’s radiation distribution law 普朗克辐射法则Pockel coefficients 普克尔斯系数Pockels cell modulator 普克尔斯调制器Pockels phase modulator 普克尔斯相位调制器Polarization transmission matrix 极化传输矩阵Polarization 极化Population inversion 粒子数反转Poynting vector 能流密度向量Preform 预制棒primary photocurrent 起始光电流principle 原理Progressive scan 全像素读出方式Propagation constant 传播常数Pumping 泵浦Pupil compensation 快门校正Pyroelectric detectors 热释电探测器Quantum efficiency 量子效率349.Smear 漏光Quantum efficiency 量子效应Quantum noise 量子噪声Quantum well 量子阱Quarter-wave plate retarder 四分之一波长延迟Radiant quantity 辐射剂量Radiant sensitivity 辐射敏感性Ramo’s theorem 拉莫定理Random noise 随机噪声Rate equations 速率方程Rayleigh criterion 瑞利条件Rayleigh scattering limit 瑞利散射极限Real image 实像Recombination lifetime 复合寿命Recombination 复合Reflectance 反射Reflection 反射Refracted light 折射光Refraction index 折射率refractive index 各向异性Refractive index 折射系数Response time 响应时间Resolving power 分辩力responsivity of InGaAs InGaAs 响应度Return-to-zero data rate 归零码Rise time 上升时间Saturation drift velocity 饱和漂移速度Saturation signal 饱和信号量Scattering 散射Second harmonic generation 二阶谐波Self-induced drift 自激漂移Self-phase modulation 自相位调制Sellmeier dispersion equation 色列米尔波散方程式separate absorption and multiplication(SAM) 分离吸收和倍增separate absorption grading and multiplication(SAGM) 分离吸收等级和倍增Shockley equation 肖克利公式Shot noise 散粒噪声Shot noise 肖特基噪声Signal to noise ratio 信噪比silicon 硅Single frequency lasers 单波长噪声Single quantum well 单量子阱Snell’s law 斯涅尔定律Solar cell 光电池Solid state photomultiplier 固态光复用器Source follower 源极跟随器Spatial filter 空间滤波器Spectral intensity 谱强度Spectral response 光谱响应Spectral responsivity 光谱响应Spontaneous emission 自发辐射stimulated emission 受激辐射Temporal resolution 动态分辨率Terrestrial light 陆地光Theraml equilibrium 热平衡Thermal generation 热再生Thermal noise 热噪声Thermal velocity 热速度Thershold concentration 光强阈值Threshold current 阈值电流Threshold voltage 阈值电压Threshold wavelength 阈值波长Total acceptance angle 全接受角Totla internal reflection 全反射Tramsmittance 传输Transfer distance 转移距离Transistor 晶体管Transit time 渡越时间Transmission coefficient 传输系数Transverse electric field 电横波场Tranverse magnetic field 磁横波场Traveling vave lase 行波激光器Tunneling effect 隧道效应Uniaxial crystals 单轴晶体UnPolarized light 非极化光Valence band 价带Vertical CCD 垂直 CCDVertical overflow drain 垂直溢出漏极Visible light 可见光Wave equation 波公式Wave number 波数Wave packet 波包络305.Wavevector 波矢量Wave 波Wavefront 波前Waveguide 波导Weak inversion 弱反转。
a r X i v :c o n d -m a t /0411745v 1 [c o n d -m a t .s t r -e l ] 30 N o v 2004Resonating Valence Bond wave function:from lattice models to realistic systems Michele Casula a ,∗Seiji Yunoki a Claudio Attaccalite a Sandro Sorella a a International School for Advanced Studies (SISSA)Via Beirut 2,434014Trieste ,Italy and INFM Democritos National Simulation Center,Trieste,Italy1IntroductionThe variational approach,by providing an ansatz for the ground state(GS)wave function of a many body Hamiltonian,is one of the possible ways to analyze both qualitatively and quantitatively a physical system.Moreover,starting from the ana-lytical properties of the variational wave function one is able in principle to under-stand and explain the mechanism underling a physical phenomenon.For instance, the many body wave function of a quantum chemical system can reveal the elec-tronic structure of the compound and show what is the nature of its chemical bonds. On the other hand,a very good variational ansatz for a model Hamiltonian helps in predicting the ground state properties and the qualitative picture of the system. In particular,Pauling[1]in1949introduced for thefirst time the concept of the resonating valence bond(RVB)ansatz in order to describe the chemical structure of molecules such as benzene and nitrous oxide;the idea behind that concept is the superposition of all possible singlet pairs configurations which link the various nuclear sites of a compound.He gave a numerical estimate of the resonating en-ergy in accordance with thermochemical data,showing the stability of the ansatz with respect to a simple Hartree Fock valence bond approach.Few decades later, Anderson[2]in1973developed a mathematical description of the RVB wave func-tion,in discussing the ground state properties of a lattice frustrated model,i.e.the triangular two dimensional Heisenberg antiferromagnet for spin S=1/2.Hisfirst representation included an explicit sum over all the singlet pairs,which turned out to be cumbersome in making quantitative calculations,the number of configura-tions growing exponentially with the system size.Much later,in1987,with the aim tofind an explanation to high temperature(HTc)superconductivity by means of the variational approach,he found a much more powerful representation of the RVB state[3],based on the Gutzwiller projection P of a BCS stateP|Ψ =PΠk(u k+v k c†k,↑c†−k,↓)|0 ,(1) which in real space and for afixed number N of electrons takes the formP|Ψ =PΣr,r′ φ(r−r′)c†r,↑c†r′,↓ N/2|0 ,(2) where the pairing functionφis the Fourier transform of v k/u k.The Cooper pairs described by the BCS wave function are taken apart from each other by the re-pulsive Gutzwiller projection,which avoids doubly occupied sites;in this way the chargefluctuations present in the superconducting ansatz are frozen and the system can become an insulator even when,according to band theory,it should be metallic. The wave function(2)allows a natural and simple description of a superconducting state close to a Mott insulator,opening the possibility for a theoretical explanation of high temperature superconductivity,a phenomenon discovered in1986[4],but not fully understood until now.Indeed,soon after this important experimental dis-covery,Anderson[3]suggested that the Copper-Oxygen planes of cuprates could be effectively described by an RVB state,and extensive developments along this lines have subsequently taken place[5].From the RVB ansatz it is clear that the HTc superconductivity(SC)is essentially driven by the Coulomb and magnetic in-teractions,with a marginal role played by phonons,in spite of their crucial role in the standard BCS theory.As far as the magnetic properties are concerned,the RVB state is quite intriguing,because it represents an insulating phase of an electron model with an odd number of electrons per unit cell,with vanishing magnetic mo-ment and without anyfinite order parameter,namely a completely different picture from the conventional meanfield theory,where it is important to break the sym-metry in order to avoid the one electron per unit cell condition,incompatible with insulating behavior.This rather unconventional RVB state is therefore called spin liquid.The structure of the paper is organized as follows:in section2we present some numerical Monte Carlo studies of lattice models,where it is shown that,once the Jastrow factor is included,the RVB wave function is able to represent an excep-tionally good ansatz for the description of the zero temperature properties of the systems studied,in very good agreement with the available experimental data.In section3,we apply the same variational wave function to quantum chemical sys-tems,in particular to benzene,where we exploit the Pauling’s idea to study in a more systematic way the role of the resonating valence bonds in this molecule, by performing realistic ab initio simulations.In the last section we make ourfinal conclusions and highlight the perspectives of this study.2Lattice modelsIn order to mimic in a simple way the essential features of a real strongly corre-lated material,a lot of lattice models have been conceived so far.One of the most important is the t−J model,which takes into account not only the charge degrees of freedom but also the magnetic superexchange interactions:H=J <i,j> S i·S j−1ing Green function Monte Carlo(GFMC)simulations within thefixed node(FN) approximation up to242sites at various doping,and by calculating the order pa-rameter P d=2lim r→∞ity is the SC order parameter P d,but since its value is of the same order as the quasiparticle weight,it can be too small to be detected with a reasonable numerical precision.Therefore,with the aim offinding a good probe for superconductivity,E. Plekhanov et al.[7]defined a new suitable quantity Z c,which measure the pairing strength between two electrons added to the GS wave function,Z c=|F(shortest distance)|/state with afinite spin gap.The distinction between the metallic and the insulating state can be made both by using the Berry phase[9]and by analyzing the behavior of the spin and charge structure factor as q→0;in all cases,the RVB state with an appropriate Jastrow factor reproduces very well the known phases.Not only the conducting properties of a strongly correlated model can be repro-duced by the RVB ansatz,but also the magnetic behavior.For instance,in the case of the t−t′1D Hubbard model,the variational wave function drives the transition from the metallic to a dimerized insulator once U/t increases.For the2D spin1/2 AFM Heisenberg model on a triangular latticeH=J <i,j>S i·S j+J′ <<i,j>>S i·S j,(7) with J being the intra chain coupling and J′the inter chain one,the RVB wave function displays a stable spin liquid behavior,due to the strong frustration of the system in the regime with J′/J=0.33.Moreover for J=0.374meV,the model is able to represent a real system,the Cs2CuCl4compound studied by Coldea et al.[10,11]who performed neutron scattering experiments in order to determine the low lying magnetic excitations.It turns out that the experimental data show an unconventional behavior of the magnetic structure of the compound,with spin-1/2fractionalized excitations and incommensurability.The numerical study carried out in Ref.[12]highlights that the incommensurability comes from the frustration of the system and it is well described by the RVB ansatz.The most impressive correspondence between the experimental data and the numerical simulations is in the spin-1excitation spectrum(see Fig.2),obtained by GFMC calculations with an RVB state used as a guiding function.As also shown in the same Fig.2,it is evident that size effects are small and the comprairson between the numerical simulation and the experiment is particularly meaningful in this case.This is possible within a Quantum Monte Carlo(QMC)scheme that allows to work with large enough systems sizes.3Realistic systemsAs we have seen in the preceding section,the RVB wave function can represent very well the GS of some strongly correlated systems,which are described by a suitable lattice model,as in the case of Cs2CuCl4.Furthermore,following the seminal idea of Pauling,the applicability of the RVB ansatz is not limited to the strongly correlated regime close to the Mott transition or to spin frustrated models, but can be extended to describe the electronic structure and the properties of real-istic systems.Indeed the quantum chemistry community has quite widely used the concept of pairing in order to develop a variational wave function able to capture0.00.51.00.01.0k x /2πE n e r g y (m e V )parison of the lowest triplet excitations,evaluated by neutron scattering experi-ments on Cs 2CuCl 4compound[11],with the QMC results,obtained using the lattice fixed node approximation and the projected BCS state to approximate the signs of the ground state wave function[12].There is no fitting parameter in the above comparison.the most significant part of the electronic correlation.Although only in 1987Ander-son discovered the link between the explicit resonating valence bond representation and the projected-BCS wave function,already in the 50’s Hurley et al.[13]intro-duced the product of pairing functions as ansatz in quantum chemistry.Their wave function was called antisymmetrized geminal power (AGP)that has been shown to be the particle conserving version of the BCS ansatz [14].It includes the sin-gle determinantal wave function,i.e.the uncorrelated state,as a special case and introduces correlation effects in a straightforward way,through the expansion of the pairing function (in this context called geminal):therefore it was studied as a possible alternative to the other multideterminantal approaches,but his success to describe correlation was very much limited,because -we believe -the Jastrow term was not included.For an unpolarized system containing N electrons (the first N/2coordinates are referred to the up spin electrons)the AGP wave function is a N 2pairing matrix determinant,which reads:ΨAGP (r 1,...,r N )=det ΦAGP (r i ,r j +N/2)for 1≤i,j ≤N/2,(8)and the geminal function is expanded over an atomic basis:ΦAGP(r↑,r↓)= l,m,a,bλl,m a,bφa,l(r↑)φb,m(r↓),(9) where indices l,m span different orbitals centered on atoms a,b,and i,j are coor-dinates of spin up and down electrons respectively.It is possible to generalize the AGP many body wave function in order to deal also with a polarized system.The geminal function may be viewed as an extension of the simple HF wave function and in fact it coincides with HF only when the number M of non zero eigenvalues of theλmatrix is equal to N/2.It should be noticed that Eq.9is exactly the pairing function in Eq.2,apart from the inhomogeneity of the former which reflects the absence of the translational invariance of a generic molecular compound.One of the main advantages of dealing with an AGP wave function is its computational cost.Indeed one can prove that expanding the geminal by adding more terms in the sum of Eq.9is equivalent to introduce more Slater determinants in the many body wave function,i.e.to have a multireference total wave function,similar to those obtained in configuration interaction(CI)or coupled cluster(CC)theories.But the computational cost of the AGP ansatz still remains the same,since one needs to compute always just a single determinant.This property is expected to be impor-tant for large scale simulations,since the number of determinants necessary for a satisfactory accuracy increases fast with the system size,limiting very much the applicability of CI and CC methods.The simplest example which shows the essence of the AGP ansatz is the H2molecule. It is well known from textbooks that molecular orbital(MO)theory at the HF level fails in predicting the binding energy and the bond length of H2,just because it overestimates the ionic terms contribution in the total wave function if the anti-bonding molecular orbitals are not included.In spite of this,the correct geminal expansion readsΦAGP(r,r′)=λφA1s(r)φA1s(r′)+φA1s(r)φB1s(r′)+A↔B,(10) whereλcan be tuned to regulate the weight of the different resonating contributions and fulfill the size consistency when the two nuclei are infinitely apart from each other(λ→0).Notice also that the chemical bond is represented in the geminal by a non vanishing value ofλbetween the orbitals centered on the two different sites between which the bond is formed.Let us consider now a gas of hydrogen dimers:in this case the geminal will contain not only the terms in Eq.10,valid for just two sites,but also the contributions from all the nuclei in the system.It is clear that the AGP wave function will allow strong chargefluctuations around each H pair,and therefore molecular sites with zero and four electrons are permitted,leading to poor variational energies.For thisreason,the AGP alone is not sufficient,and it is necessary to introduce a Gutzwiller-Jastrow factor in order to dump the expensive chargefluctuations.Moreover only the AGP-Jastrow(AGP-J)wave function is the real counterpart of the RVB ansatz of strongly correlated lattice models,since the projection is essential to get the correct distribution of the pairing in the compound.The AGP-J wave function has shown to be effective both in atomic[15]and in molecular systems[16].Both the geminal and the Jastrow play a crucial role in determining the remarkable accuracy of the many body state:the former permits the correct treatment of the nondynamic correlation effects,the latter allows the local conservation of charge in a complex molecular system and also to fulfill the cusp conditions which make the geminal expansion rapidly converging to the lowest possible variational energies.The study of the AGP-J variational ansatz with the inclusion of two and three body Jastrow factors is possible by means of QMC techniques,which can deal explicitly with correlated wave functions.The optimization procedure,necessary to reach the lowest variational energy within the given variational freedom,is feasible also in a stochastic Monte Carlo framework,after the recent developments in thisfield ([17,18]).Benzene is the largest compound we have studied so far;in order to represent its 1A1g GS we have used a very simple one particle basis set:for the AGP,a2s1p double zeta(DZ)Slater set centered on the carbon atoms and a1s single zeta(SZ) on the hydrogen.For the3-body Jastrow,a1s1p DZ Gaussian set centered only on the carbon sites has been chosen.We started from a non resonating2-body Jastrow wave function,which dimerizes the ring and breaks the full rotational symmetry, leading to the Kekul´e configuration.As we expected,the inclusion of the resonance between the two possible Kekul´e states lowers the variational Monte Carlo(VMC) energy by more than2eV.The wave function is further improved by adding another type of resonance,that includes also the Dewar contributions connecting third near-est neighbor carbons.As reported in Tab.1,the gain with respect to the simplest Kekul´e wave function amounts to4.2eV,but the main improvement arises from the further inclusion of the three body Jastrow factor,which allows to recover the 89%of the total atomization energy at the VMC level.The main effect of the three body term is to keep the total charge around the carbon sites to approximately six electrons,thus penalizing the double occupation of the p z orbitals.A more clear behavior is found by carrying out diffusion Monte Carlo(DMC)sim-ulations:the interplay between the resonance among different structures and the Gutzwiller-like correlation refines more and more the nodal surface topology,thus lowering the DMC energy by significant amounts.Therefore it is crucial to insert into the variational wave function all these ingredients in order to have an adequate description of the molecule.For instance,in Fig.3we report the density surface difference between the non-resonating3-body Jastrow wave function,which breaks the C6rotational invariance,and the resonating Kekul´e structure,which preserves the correct A1g symmetry:the change in the electronic structure is significant.Thebest result for the binding energy is obtained with the Kekul´e Dewar resonating 3body wave function,which recovers the 98,6%of the total atomization energy with an absolute error of 0.84(8)eV .As Pauling [1]first pointed out,benzene is a genuine RVB system,indeed it is well described by the AGP-J wave function.-0.05-0.025 0 0.0250.056ρ(r) resonating Kekule - ρ(r) non resonating4-0.05-0.0250.0250.051/a 2y Fig.3.Electron density (atomic units)projected on the plane of C 6H 6.The surface plot shows the difference between the resonating valence bond wave function,with the correct A 1g symmetry of the molecule,and a non-resonating one,which has the symmetry of the Hartree–Fock wave function.Table 1Binding energies in eV obtained by variational (∆V MC )and diffusion (∆DMC )Monte Carlo calculations with different trial wave functions for benzene.In order to calculate the binding energies yielded by the two–body Jastrow,we used the atomic energies reported in Ref.[15].The percentages (∆V MC (%)and ∆DMC (%))of the total binding energies are also reported.Data are taken from Ref.[16].4ConclusionsIn this paper we have described a very powerful variational ansatz that has been introduced to understand the properties of strongly correlated materials just after the discovery of HTc superconductivity.We have shown that the RVB wave func-tion paradigm is not only useful for describing the GS and low lying excitations of lattice models,such as Heisenberg or t−J model,but is also suited for approach-ing realistic systems,by considering explicitly the long range Coulomb repulsion and the full quantum mechanical interaction among electrons within the Born-Oppenheimer approximation.Moreover,by using the same type of wave function both for lattice model and realistic system,it is possible to have some insight in the electron correlation behind the latter and to check the reliability of the model in predicting the properties of a real compund.For instance the benzene molecule can be idealized by a six site ring Heisenberg model with one electron per site,in order to mimic the out of plane bonds of the real molecule,coming from the p z electrons and leading to an antiferromagnetic superexchange interaction between nearest neighbor carbon sites.We have studied in this case the spin–spin correla-tionsC(i)= S z0S z i ,(11) where the index i labels consecutively the carbon sites starting from the reference 0,and the dimer–dimer correlationsD(i)=D0(i)/C(1)2−1,D0(i)= (S z0S z1)(S z i S z i+1) .(12)Both correlation functions have to decay in an infinite ring,when there is neither magnetic(C(i)→0),nor dimer(D(i)→0)long range order as in the true spin liquid ground state of the1D Heisenberg infinite ring.Indeed,as shown in the inset of Fig.(4),the dimer–dimer correlations of benzene are remarkably well reproduced by the ones of the six site Heisenberg ring,whereas the spin–spin correlation of the molecule appears to decay faster than the corre-sponding one of the model.Though it is not possible to make conclusions on long range properties of afinite molecular system,our results suggest that the benzene molecule can be considered closer to a spin liquid,rather than to a dimerized state, because,as well known,the Heisenberg model ground state is a spin liquid and displays spontaneous dimerization only when a sizable next-nearest frustrating su-perexchange interaction is turned on.[19]As any meaningful variational ansatz,the RVB approach naturally brings a new way of understanding the many-body problem,as for instance the Hartree-Fock-0.2-0.10.1 0.20.3 0 1 2 3s p i n s p i n distance on the ring Fig.4.Spin–spin correlation function for benzene (full squares)and for the Heisenberg model (empty circles).In the inset,also the dimer–dimer correlation function is reported with the same notation.For the benzene molecule,these correlation are obtained by a coarse grain analysis in which the “site”is defined to be a cylinder of radius 1.3a 0centered on the carbon nuclei,with a cut off core (i.e.we considered only the points with |z |>0.8a 0).All the results are pure expectation values obtained from forward walking calculations.theory helped to interpret the periodic table of elements,or to establish on theo-retical grounds the band theory of insulators.With the RVB paradigm,many un-usual phenomena now appear to be possibly explained in a simple and consistent framework:the role of correlation in Mott insulators,or the explanation of HTc superconductivity,and finally the fractionalization of spin excitations,which was supposed to take place only in quasi-one dimensional systems,and instead it has been recently detected in higher dimensions.[10]All these phenomena cannot be understood not even qualitatively within a mean field Hartree–Fock theory,as the important ingredient missing in the latter approach is just the correlation,that can lead to essentialy new effects.In our opinion the RVB wave function is a natural extension of the Hartree-Fock one,to which it reduces whenever the correlation term is switched off.In some sense the determinantal part is useful to represent the electronic density and all the one body properties of an electronic system.On the other hand the Jastrow term is necessary to take correctly into account the density–density correlation,N (r )=<n 0n r >.The long range behavior of N (r )discriminates a metal,dis-playing Friedel oscillations at 4k F where k F is the Fermi momentum,from an insulator,which shows an exponentially localized correlation N (r )≃exp(−r/ξ),where ξis the corresponding characteristic length.The Jastrow correlation can be-come non trivial when the determinantal part acquires a non conventional meaning. For instance,the determinantal part in the RVB wave function could describe a su-perconductor or a metal,but the presence of the Jastrow factor is able to turn the system into an insulator,by correlating the electrons in a non trivial way.On the other hand,superconductivity can naturally become stable in a system with only repulsive interactions,despite the BCS theory would require an effective attraction mediated by the phonons.For all the above reasons we believe that it is the right time to make an effort to study complex electronic systems by means of this new paradigm,especially for discovering new challenging effects in which the role of correlation is dominant. 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