下载文档原格式
- 1 - 量子退相干 科学家近日公布了一项最新研究成果，他们发现某些粒子能够传送声音，即使是极短距离也可以。我有点疑惑，为什么声波可以传播呢？难道我们听到的所有声音都是量子共振的结果吗？那这个世界不就太神奇了吗？ 0.1秒的时间里，分子竟然会“跳”近两万次 如果用超级计算机对比当时同一房间内发生的图像，就会发现它们看起来会有细微的差别。这些差别表明，分子并非一下子消失无踪，而是通过跳跃式运动将“某些东西”留下了。这种行为，科学家称之为“量子退相干”。简单来说，这意味着一旦碰到障碍物，分子中的电子就会被卡住。所谓“电子”，实际上是带负电荷的原子核。当电子被困于一定区域后，电子就会产生一个足够高的能量，从而逃脱。而在这一过程中，它们同时又会打出一个电子来。这种“二次退相干”就是让分子跳跃的原因。因为碰撞次数越多，粒子留下的痕迹就越少。 同样的，在冰块周围，热气体的温度会迅速升高，冰块开始融化。原因则是热气体分子发生“量子退相干”的缘故。热气体分子首先因其量子特性而发生一次“二次退相干”，由此形成一种叫做“冷阱”的结构。这种结构会迫使它们放弃已经占据的位置，而飞奔到更靠近冰块的地方去。另外，这种行为在雪花的生长过程中也会发生。热气体分子在加热的过程中产生很多“冷阱”，当它们靠近这些“冷阱”时，就会将它们排挤出来，使雪花的表面积增大。雪花在向阳光照射的方向伸展，吸收阳光中的能量，慢慢地形成降落伞，完成自己的使 - 2 -
命。 在实验中，两位德国物理学家从容器中释放出一束激光，光线通过一面透明玻璃墙反射回来，落在两只石英玻璃管中。它们发现激光落在玻璃管中的一只后，就再也不会返回玻璃管中了。于是，他们就设计了一台测量仪器，来探测这些返回光线的走向和强度。科学家用超级计算机进行了演示，结果发现，随着时间流逝，这束激光似乎越来越弱。结果，这种现象被称为“绝对消失”。但这并不意味着一束激光永远消失了，而是它逐渐变得极其微弱，人眼几乎察觉不到。研究者认为，这种现象正好可以用来解释“量子力学与实验的预测差距”。目前还没有人能够合理解释这一效应的成因，它的出现很可能只是偶然事件。
灰体辐射问题的探究摘要：在工程计算中常用灰体辐射模型来计算辐射传热，然而在大学本科教学中极少出现对灰体辐射的详细解法的讨论。
文章对一道典型的灰体辐射题目进行了多种解法的探讨，为灰体辐射传热教学提供参考。
关键词：传热学；教学方法中图分类号：G642.0文献标志码：A 文章编号：1674-9324（2020）08-0323-02收稿日期：2019-05-31作者简介：郭俊宏（1986-），男（汉族），江苏南京人，博士，讲师，研究方向：光热转换及光通信方向。
在热辐射分析中，把光谱吸收比与波长无关的物体称为灰体（gray body ）[1]。
对工程计算而言，只要在所研究的波长范围内光谱吸收比基本上与波长无关，则可以按灰体的假定来简化处理。
因此灰体辐射问题在传热学的教学中是重点部分之一。
实际教学过程中，学生对知识点较容易理解，但遇到具体计算问题时，仍难找到合适方法解决。
另外，在近几年的高中物理竞赛和各高校的自主招生考试中，也逐渐出现关于简单的灰体计算问题。
在此之前，各种参考书上关于灰体辐射模型的讲解和练习都比较少，很多同学在学习中感到无从下手。
因此我们以一道经典灰体辐射题目为例，探讨其多种解法。
原题：太空中有一由同心的内球和球壳构成的实验装置，内球和球壳内表面之间为真空。
内球半径为r=0.200m ，温度保持恒定，比辐射率为e=0.800；球壳的导热系数为κ=1.00×10-2J ·m -1·s -1·K -1，内、外半径分别为R 1=0.900m 、R 2=1.00m ，外表面可视为黑体；该实验装置已处于热稳定状态，此时球壳内表面比辐射率为E=0.800。
斯特藩常量为σ=5.67×10-8W ·m -2·K -4，宇宙微波背景辐射温度为T=2.73K 。
若单位时间内由球壳内表面传递到球壳外表面的热量为Q=44.0W ，球壳外表面温度T 2=88.6K ，内表面温度T 1=128K ，求内球温度T0。
Thermodynamics a nd S ta1s1cal M echanicsSpring 2012Lecture 1Introduc1on t o T hermodynamicsDimi C ulcer微尺度11－002dimi@Office h ours: b y a ppointmentMy E nglish• e.g. = f or e xample • i.e. = t hat m eans • certain ~ 某 • assignment = h omework • mean = a verage • You c an s peak i n C hinese (slowly) • You c an s end e mail i n C hinese • Assignments a re i n E nglish • You c an a nswer i n C hinese• the U K = B ritain • the U S = A merica • TA = t eaching a ssistant • 帮教 • phenomenon, p henomena• momentum, m omentaSome w ords• fundamental a dj . 基础的,必要的; n . 基本法则• empirical 以观察或实验为依据的• law 定律• principle 原理• to v iolate 违反,违背• equa1on 方程• func1on 函数• variable a dj. 可变的; n . 变量• constant 常数• thermometer 温度计• macroscopic 宏观的• microscopic 微观的• arbitrary 任意的 • aVrac1ve 吸引的 • repulsive 排斥的 • Infinitesimal 极微小的 • concept 概念 • parameter 参数 • maVer 物质 • characterize 表征,描绘 • propor1onal 成比例的 • phenomenological 唯象的• concrete 实体的 • abstract 抽象的 • en1ty 实体 • deriva1on 衍生，派生State o f m aVer a nd p hase• High-‐school p hysics u nderstanding• There a re 3 s tates o f m a)er• Solid, l iquid a nd g as• More g enerally, a s tate i s c alled a p hase• Solid p hase• Liquid p hase• Gas p hase o r g aseous p hase• Phase i s a m ore g eneral, m ore u seful c oncept • For e xample F e b ecomes f erromagne1c b elow T c• We s peak o f a n o rdinary p hase a nd a f erromagne1c p hase • Right n ow t his i s j ust v ocabulary• Later y ou w ill l earn t he p hysical d ifferenceWhat i s t hermodynamics?• Thermodynamics i s a m acroscopic t heory • It d escribes l arge, m any-‐par1cle s ystems• Thermodynamics h as t wo t asks• Define a ppropriate p hysical q uan11es i n o rder t ocharacterize m acroscopic p roper1es o f m aVer• Relate t hese q uan11es b y a s et o f e qua1ons, w hich a reuniversally v alid (i.e. d o n ot d epend o n s pecific s ystem) • Thermodynamics i s p henomenological• It t akes i ts c oncepts d irectly f rom e xperiments• Thermodynamics i s a ll c lassical p hysics• No q uantum m echanics• We d o n ot t alk a bout a toms, m oleculesThermodynamics & S ta1s1cal M echanics• Sta1s1cal m echanics i s a m icroscopic t heory • We c are a bout t he d ynamics o f i ndividual p ar1cles• Sta1s1cal m echanics h as t wo b ranches• Classical s ta1s1cal m echanics• Quantum s ta1s1cal m echanics• We w ill s tudy b oth i n t his c ourse• Sta1s1cal m echanics h elps u s t o l ink t he p hysical laws o f t he m icroscopic w orld w ith t hose o f t he macroscopic w orld• One p ar1cle – m echanics• Many p ar1cles – s ta1s1csApplica1ons o f t hermodynamics • Thermodynamics h as m any a pplica1ons• Chemical r eac1ons• Phase t ransi1ons» e.g. s olid t o l iquid, l iquid t o g as» Can b e m ore c omplicated• Solid s tate» Magne1sm» Superconduc1vity a nd s uperfluidity (e.g. l iquid H e)» Charge a nd h eat t ransport• Stars, e.g. t he f orma1on o f s tars, C handrasekhar l imit• The a tmosphere, w eather, c limate• Biology e.g. l ife• All t hese s ystems o bey c ommon & g eneral l awsOverview o f t hermodynamics • In t he first p art o f t he c ourse w e w ill s tudy • The l aws o f t hermodynamics» 0, 1, 2, 3» These a re v ery g eneral• Phase t ransi1ons» Solid t o l iquid t o g as» Paramagne1c t o f erromagne1c» These a re c alled c ri1cal p henomena• Non-‐equilibrium t hermodynamics» Heat t ransport• Kine1c t heory o f g ases» Explains p, V, T b y c onsidering d ynamics o f p ar1clesImportant c oncepts i n t hermodynamics • Thermodynamic s ystem• Dynamical s ystem w ith m any d egrees o f f reedom• Any m acroscopic s ystem i s a t hermodynamic s ystem • Environment = s urroundings = e verything e lse • Thermodynamic p arameters• Measurable m acroscopic q uan11es a ssociated w ith s ystem• Pressure, v olume, t emperature• Thermodynamic s tate• Specified b y a s et o f a ll v alues o f a ll t he t hermodynamicparameters n ecessary t o d escribe t he s ystemIsolated, c losed, a nd o pen s ystems • Isolated s ystem (idealized)• Does n ot i nteract w ith t he e nvironment i n A NY w ay• Separated b y a w all (par11on) w hich d oes n ot a llowexchange o f h eat o r p ar1cles (maVer)• Total e nergy, v olume a nd p ar1cle n umber a re c onserved • Closed s ystem• Can e xchange e nergy w ith t he e nvironment• Cannot e xchange p ar1cles w ith t he e nvironment• Par1cle n umber i s c onserved• Total e nergy i s n ot c onserved• If c losed s ystem i n e quilibrium w ith e nvironment» Total e nergy h as a verage v alue r elated t o t emperature o fenvironment» Can u se t emperature t o c haracterize s tate o f s ystemIsolated, c losed, a nd o pen s ystems • Open s ystem• Can e xchange e nergy a nd p ar1cles w ith t he e nvironment• Total e nergy n ot c onserved• Par1cle n umber n ot c onserved• If o pen s ystem i n e quilibrium w ith e nvironment» Total e nergy h as a verage v alue r elated t o t emperature o fenvironment» Par1cle n umber h as a verage v alue r elated t o t emperature o fenvironment» Can u se t emperature t o c haracterize s tate o f s ystem» Can a lso u se c hemical p oten1al t o c haracterize t he s ystem» We w ill d efine t he c hemical p oten1al l ater• Right n ow w e a re u sing t he w ord t emperature • Later w e w ill d efine i t p roperlyHomogeneous s ystems• Homogeneous s ystem• The p roper1es o f t he s ystem a re t he s ame f or a ny p art • Heterogeneous s ystem• The p roper1es o f t he s ystem c hange d iscon1nuously a tcertain s urfaces• A h eterogeneous s ystem h as h omogeneous p arts • Different p arts o f t he s ystem a re i n d ifferent p hases• Phase b oundary• One s ystem, d ifferent p hases• e.g. p ot c ontaining w ater, a ir a nd s team• There a re t wo p hases – l iquid p hase a nd g aseous p hase• The b oundary b etween t hem i s c alled p hase b oundaryThermodynamic e quilibrium• Think o f a n i solated s ystem• The s ystem i s l ej s tanding f or a l ong 1me• It c omes t o a final s tate w hich d oes n ot c hange • Thermodynamic p arameters a re c onstant• The s ystem i s i n t hermodynamic e quilibrium i f i ts thermodynamic s tate d oes n ot c hange w ith 1me • A t hermodynamic s tate i s a n e quilibrium s tate • Thermodynamic e quilibrium• Also c alled t hermal e quilibrium• Ojen j ust e quilibriumThermal e quilibrium o f t wo s ystems • Generally c onsider t wo i solated s ystems A a nd B • Bring A a nd B i nto c ontact w ith e ach o ther• Ajer a l ong 1me t he t otal s ystem A+B r eaches e quilibrium• Then A a nd B a re i n e quilibrium w ith e ach o ther• A a nd B a re a lso (separately) i n t hermal e quilibrium • Think o f a c losed s ystem• A c losed s ystem e xchanges h eat w ith t he e nvironment• We c an t hink o f t he e nvironment a s a h eat b ath• e.g. t ea o n t able• Ajer a l ong 1me t emperature o f t ea = r oom t emperature• Tea i s i n t hermodynamic e quilibrium w ith r oom• Macroscopic v ariables w hich h ave a d efinite value f or e ach e ach s tate o f t hermal e quilibrium • State v ariables a re d efined o nly i n e quilibrium • Can b e m easured o nly i n e quilibrium• Usually w e o nly n eed a f ew (e.g. 3-‐4) s tate variables t o s pecify t he s tate o f a s ystem• Microscopic q uan11es a re N OT s tate v ariables • posi1on• velocity• momentum• Heat a nd w ork a re a lso N OT s tate v ariables• State v ariables c an b e • Pressure p• Volume V• Temperature T• Energy E (or U)• Entropy S• Par1cle n umber N• Chemical p oten1al μ• Total c harge Q• Total d ipole m oment P• Magne1za1on M• Refrac1ve i ndex ε• Viscosity o f a fluid• Chemical c omposi1onIntensive a nd e xtensive v ariables • Extensive q uan1ty• Scales w ith s ystem s ize• Propor1onal t o t he a mount o f m aVer i n t he s ystem• They a re a ddi1ve• Volume, e nergy, p ar1cle n umber, e ntropy• Intensive q uan1ty• Independent o f t he s ize o f t he s ystem• Independent o f t he a mount o f m aVer i n t he s ystem• Pressure, t emperature, d ensity• Also r efrac1ve i ndex a nd o thers• Can b e d efined l ocally (i.e. f unc1on o f r)• But m ost o f t he 1me w e a ssume t hem t o b e u niformEqua1on o f s tate• Func1onal r ela1onship b etween s tate v ariables • It d escribes a s ystem i n e quilibrium• For e xample i f p arameters a re p, V a nd T• There i s s ome f unc1on f(p, V, T) s uch t hatf(p,V,T)=0• Reduces n umber o f i ndependent p arameters f rom 3 t o 2• f i s g iven w hen t he s ystem i s s pecified = s tate f unc1on• State o f s ystem i s a p oint i n p, V, T s pace• Equa1on o f s tate d efines a s urface i n t his s pace• Any p oint o n t he s urface i s a s tate i n e quilibrium• Other p arameters – o ther s paces, p oints, s urface• Experimentally• All g ases b ehave i n a u niversal w ay w hen t hey a resufficiently d ilute = w hen t he d ensity i s l ow e nough • Ideal g as• Idealiza1on o f t his d ilute l imit• Par1cles a re p oint-‐like (i.e. h ave z ero s ize)• No i nterac1ons b etween p ar1cles• An i deal g as i s a n i dealized s ystem• Parameters f or i deal g as• p, V, T, N• Boyle’s l aw (1664) – a t c onstant t emperaturepV= constant = pVpV =nRT • Ideal g as e qua1on o f s tate• Defines i deal g as t emperature s cale• Like h igh-‐school p hysics• Ideal g as – H e a t v ery l ow d ensity• Measure p V/Nk o f i deal g as a t T a t w hich w ater b oils • Also m easure a t T a t w hich w ater f reezes• Draw a s traight l ine c onnec1ng t hem• Divide i nto 100 u nits – t his i s t he K elvin s cale• How t o u se• Bring o bject i n c ontact w ith i deal g as• Measure p V o f i deal g as• Read o ff t he t emperatureMore a bout t hermometers• Remember• Measuring t emperature i s r elated t o t he e qua1on o f s tate • To d efine a s cale• Choose T0 = 273.15K i n h onour o f K elvin• p0, V0 a re g iven i n y our t extbook• Celsius T C• Water f reezes = 0• Water b oils = 100• Fahrenheit T F• T F = 1.8 T C + 32• T F = T C at -‐40 d egrees• Degrees C elsius a nd d egrees F ahrenheit• But K elvin, n ot d egrees K elvinZeroth l aw o f t hermodynamics • If• System A i s i n e quilibrium w ith s ystem B• System B i s i n e quilibrium w ith s ystem C• Then• System A i s i n e quilibrium w ith s ystem C• Two s ystems A a nd B i n e quilibrium• Func1ons o f s tate f A a nd f B• See b lackboard f or d eriva1on• Systems i n t hermal e quilibrium• They h ave a c ommon i ntensive q uan1ty – t emperature• Systems n ot i n e quilibrium h ave d ifferent t emperatures • See b lackboard f or d eriva1on• First t ake t he i deal g as e qua1on o f s tate• Real g as – p hysical c onsidera1ons• First, p roper v olume• V i s n ot a c onstant b ecause V → 0 a s T → 0• Change V t o V – N b, w here b i s s ome p arameter• Second, i nterac1ons b etween p ar1cles• Interac1on i s m ainly a Vrac1ve• Consider a g lobe w ith a d ensity N/V• Inside t he g lobe t he a verage f orce b etween p ar1cles i s 0• But n ear t he w alls t his i s n ot t rue• Par1cles o n s urface f eel n et f orce t owards i nside• So p f or r eal g as i s s maller t han f or i deal g as• p ideal = p real + p0Exact a nd p ar1al d ifferen1als• State f unc1on = f unc1on o f m any v ariables • We m ake u se o f e xact a nd p ar1al d ifferen1als• For e xample i n e quilibriumf(p,V,T)=0• This m eans w e c an r egard p=p(V,T), V=V(p,T) a nd T=T(p,V) • Differen1al a lso c alled d eriva1ve• Total d eriva1ve, t otal d ifferen1al• See b lackboard f or d eriva1onTypes o f p rocesses• Infinitesimal p rocess• Difference b etween i ni1al a nd final s tate i s i nfinitesimal • Quasi-‐sta1c p rocess (ideal p rocess)• System a nd s urroundings m aintain t hermal e quilibrium• Change m ust b e s low e nough – S LOW p rocess• Quasi-‐sta1c p rocesses a re r eversible – a p rocess i sreversible i f i t r etraces i ts h istory i n 1me w hen t he e xternalcondi1ons r etrace t heir h istory i n 1me• Isothermal• Constant t emperature• Adiaba1c• No t hermal c ontact w ith t he s urroundings• However w ork i s d one o n t he s urroundings o r b y t hesurroundingsThermocouple 热电偶• Seebeck effect – t hermoelectric effect• Temperature d ifference g enerates v oltage i n c onductor• Join s econd c onductor t o m easure t he v oltage• Second c onductor h as o pposite effect• But i f m aterial i s d ifferent n et c urrent flows ∝ T• Used a s a t emperature s ensor• Useful b ecause• Ac1ve o ver w ide r ange o f t emperatures – 000s o f d egrees• Powers i tself• However• Not v ery a ccurate – n ot s ensi1ve b y m ore t han 1 d egree• So y ou c an u se i t w hen y ou d o n ot n eed m uch p recision• e.g. g as t urbine, d iesel e ngine, k iln (=oven), i ndustrySummary• Isolated, o pen a nd c losed s ystems• Thermodynamic e quilibrium• Intensive a nd e xtensive v ariables• State v ariables a nd e qua1on o f s tate • Ideal g as – n o i nterac1ons• Van d e W aals g as – w eak i nterac1ons • Temperature – t hermodynamic d efini1on • Thermometer• Assignments w ill b e g iven n ext w eek。
玻色爱因斯坦凝聚研究进展玻色-爱因斯坦凝聚（Bose-Einstein condensation，简称BEC）是一种量子物理现象，最早由印度物理学家苏蒂斯·玻色（Satyendra Nath Bose）和爱因斯坦在1924年预言。
在一些条件下，一组玻色子（具有整数自旋的粒子）能够凝聚为一个量子态，所有粒子都处在同一个基态中，形成一个宏观的量子态。
在玻色-爱因斯坦凝聚中，粒子的量子性质变得非常显著。
通常情况下，粒子遵循波动方程，其行为可以由经典波动模型所描述。
然而，在准确的低温条件下，当粒子的波长比粒子之间的距离大得多时，波动性开始显现。
此时，波函数可以描述粒子的位置和动量的不确定性，并且整个系统处于一种相干态。
最早的实验证实了玻色-爱因斯坦凝聚的存在是在1995年由美国科学家埃里克·考伦（Eric Cornell）和卡尔·魏曼（Carl Wieman）以及德国科学家沃尔夫冈·凯特勒（Wolfgang Ketterle）的研究小组在铷原子上实现的。
他们使用冷却技术将铷原子冷却到几乎绝对零度（温度接近绝对零度的冷冻状态）。
在这个极低的温度下，原子的动力学行为可以由玻色-爱因斯坦统计学描述，因此可能形成凝聚态。
他们通过激光冷却和磁场梯度冷却的方法将铷原子冷却到非常低的温度，进而实现了玻色-爱因斯坦凝聚。
自那时以来，关于玻色-爱因斯坦凝聚的研究逐渐深入。
科学家们发现，不仅可以在铷原子上实现玻色-爱因斯坦凝聚，还可以在其他类型的玻色子上实现，包括钠、锂、铯等碱金属原子以及氢气分子和磁光线性晶体等。
在实验研究方面，科学家们还在探索如何调控和操纵凝聚体的性质。
利用电场和磁场的方法，他们可以改变凝聚体的密度和形状，进而改变玻色子之间的相互作用。
他们还通过激光的束缚和操作可以观察和测量凝聚体的运动和行为，甚至可以制备出玻色子的超流体和制造出相干光。
在理论研究方面，科学家们对玻色-爱因斯坦凝聚的性质和行为进行了深入的研究。
