玻色-爱因斯坦凝聚

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1、专题三：玻色－爱因斯坦凝聚经典统计分布函数量子统计分布函数玻色－爱因斯坦凝聚经典统计分布函数一绝热系统处在势场中：一个服从经典统计的系统处于温度T的热平衡中，其能量的每一独立的平方项都有平均值1/2kT.与b无关！如粒子动力学只容许分立能量：普朗克能量均分定理利用它可推导出黑体辐射公式2.量子统计分布函数两个全同粒子，推广到n个全同粒子（玻色子），n个玻色子处于相同状态的几率n！倍于其经典几率。问题：将一个玻色子放在一个状态上去的几率和状态原有的玻色子数目有何关系？再放一个的几率是相应经典几率的(n+1)倍，增强因子（1+n）费米

2、子：为得量子统计分布，还需精细平衡原理。在处于平衡的体系中考虑两个能级i与j,上面分别有ni及nj个粒子。令Ri->j代表从i到j的跃迁几率。精细平衡：经典统计，有：对玻色子，有增强因子1+n:对所有能级成立。费米子：1－n取代1+n玻色－爱因斯坦分布函数费米－狄拉克分布函数QuantumStatisticsPredicted1924……Created19953.玻色－爱因斯坦凝聚Q1:WhatIsBose-EinsteinCondensation?DeBroglie德布罗意(1929NobelPrizewinner)propo

3、sedthatallmatteriscomposedofwaves.Theirwavelengthsaregivenby=deBrogliewavelengthh=Planck’sconstant普朗克常数m=massv=velocityAgainstOurIntuition?!Inmosteverydaymatter,thedeBrogliewavelengthismuchshorterthanthedistanceseparatingtheatoms.Inthiscase,thewavenatureofatomscannotb

4、enoticed,andtheybehaveasparticles.ThewavenatureofatomsbecomenoticeablewhenthedeBrogliewavelengthisroughlythesameastheatomicdistance.Thishappenswhenthetemperatureislowenough,sothattheyhavelowvelocities.Inthiscase,thewavenatureofatomswillbedescribedbyquantumphysics,e.g.

5、theycanonlystayatdiscreteenergystates(energyquantization).BoseandEinsteinIn1924anIndianphysicistnamedBosestudiedthequantumbehaviourofacollectionofphotons.BosesenthisworktoEinstein,whorealizedthatitwasimportant.Einsteingeneralizedtheideatoatoms,consideringthemasquantum

6、particleswithmass.Einsteinfoundthatwhenthetemperatureishigh,theybehavelikeordinarygases.However,whenthetemperatureisverylow,theywillgathertogetheratthelowestquantumstate.ThisiscalledBose-Einsteincondensation.Fermions(費米子)andBosons(玻色子)NotallparticlescanhaveBEC.Thisisr

7、elatedtothespinoftheparticles.Thespinquantumnumberofaparticlecanbeanintegerorahalf-integer.Singleprotons,neutronsandelectronshaveaspinof½.Theyarecalledfermions.Theycannotappearinthesamequantumstate.BECcannottakeplace.Someatomscontainanevennumberoffermions.Theyhaveatot

8、alspinofwholenumber.Theyarecalledbosons.Bosonsshowstrong“social”behaviour,andcanhaveBEC.Example:A23Naatomhas11protons,12neut