当前位置：文档之家 › Popov approximation for composite bosons in the BCS-BEC crossover

Popov approximation for composite bosons in the BCS-BEC crossover

  • 格式：pdf
  • 大小：293.15 KB
  • 文档页数：13

arXiv:cond-mat/0407728v1 [cond-mat.supr-con] 28 Jul 2004PopovapproximationforcompositebosonsintheBCS-BECcrossoverP.PieriandG.C.StrinatiDipartimentodiFisica,UdRINFM,Universit`adiCamerino,I-62032Camerino,Italy(Dated:February2,2008)

TheoreticaltreatmentsoftheBCS-BECcrossoverneedtoprovideasaccurateaspossibledescrip-tionsofthetworegimeswherethedilutenessconditionapplies,eitherintermsoftheconstituentfermions(BCSlimit)orofthecompositebosonswhichformasbound-fermionpairs(BEClimit).Thishastooccurviaasinglefermionictheorythatbridgesacrossthesetwolimitingrepresenta-tions.Inthispaper,wesetupsuccessiveimprovementsofthefermionictheory,thatresultintocompositebosonsdescribedatthelevelofeithertheBogoliubovorthePopovapproximationsforpoint-likebosons.ThisworkbearsontherecentexperimentaladvancesontheBCS-BECcrossoverwithtrappedFermiatoms,whichshowtheneedforaccuratetheoreticaldescriptionsofBECsideofthecrossover.

PACSnumbers:03.75.Ss,03.75.Hh,05.30.Jp

I.INTRODUCTIONRecentexperimentaladvances1,2withultracoldtrappedFermiatomshaveproducedsystemsofcompos-itebosons(dimers),wherepairsoffermionsbindduetotheirstrongmutualattractioninducedbyaFano-Feshbachresonance3.Contrarytothecaseofpoint-likebosons,forwhichtheinternalfermionicstructureisim-material,forthecompositebosonstheinternalfermionicstructureisrelevanttotheextentthattheirbindingenergyiscomparablewiththeenergyandtemperaturescalesinvolvedintheexperiments.Theoreticaldescrip-tionsofthecompositebosonsshouldthustakeintoac-countnotonlytheiroverallbosonicstructure(associatedwiththeircenter-of-massmotion),butalsotheircom-positenatureintermsofthedegreesoffreedomoftheconstituentfermions.AnysensibletheoreticalapproachtotheBCS-BECcrossovershouldrelyonasingletheory,thatrecoverscontrolledapproximationsonbothsidesofthecrossoverandprovidesacontinuousevolutionbetweenthem.Inapreviouspaper4,theapproachoriginallydevelopedbyPopovforaweakly-interacting(dilute)superfluidFermigas5wasimprovedbyincludingtheeffectsoftheBogoliubov-Andersonmode6inthediagonalfermionicself-energy.Withthisgeneralization,itwasalsoshown4

that,inthestrong-couplinglimitofthefermionicattrac-tion,thesametheoryisabletodescribeadilutesystemofcompositebosonswithintheBogoliubovapproximation7.TheoreticalworkonthecondensatesofdilutetrappedBosegases8,9hasshownthatanaccuratedescriptionoftheexperimentaldatacanbeobtainedbyusingtheso-calledPopovbosonicapproximation5.Thisapproxima-tionleadstoimprovementsovertheBogoliubovapprox-imation,inthatittreatsthedensitiesofnoncondensedandcondensedatomsonthesamefooting,atleastinthetemperaturerange(belowthecriticaltemperature)wherethetwodensitiesarecomparabletoeachother.IthasbeenshownthattheuseofthePopovbosonicap-proximationisespeciallyrelevanttothethermodynam-icsoftrappedBoseatoms8.Itleads,inparticular,to

adownwardshiftofthecriticaltemperature10,whichhasbeenrecentlymeasuredwithgreataccuracy11.ThePopovbosonicapproximationwasoriginallyconceivedforahomogeneousgas5;itsextensiontoaninhomoge-neousgaswasdescribedindetailinRef.12.

PurposeofthepresentpaperistodeviseafermionicapproximationfortheBCS-BECcrossoverinthebroken-symmetryphase,whichinthestrong-couplinglimitofthefermionicattractionrecoversthePopovapproxima-tionforthecompositebosons.WeshallarrivetothisPopovapproximationbysuccessiveimprovementsofthefermionictheory,startinginitiallyfromtheBCSmean-fieldapproximationandthenincludingfluctuationsoverandaboveitatdifferentlevelsofsophistication.ThetheorydescribedalreadyinRef.4(seealsoRef.13)willberecoveredasanintermediatestepofthisprocess.ItwillturnoutthatthePopovdescriptionofthecompos-itebosonsonthestrong-couplingsideofthecrossovercorrespondstoincludingpseudo-gapeffectsontopoftheBCSapproximationinthefermionictwo-particleGreen’sfunctionontheweak-couplingsideofthecrossover.Im-provementsofthetheoryonthestrong-couplingside,astogetamoreaccuratedescriptionofthescatteringprocessesbetweenthecompositebosons,willbefurtherconsideredalongthelinesofRef.14.Theissuetorefinethetheoryontheweak-couplingside,astoincludeallpossiblecontributionstoanimperfectFermigas15,willinsteadbethesubjectoffuturestudy.

Inthefollowing,thetheoryoftheBCS-BECcrossoverwillbeconsideredforahomogeneoussystem.Extensiontotrappedgasesmaybedone,inpractice,byconsider-ingalocal-densityapproximation,wherebythefermionicchemicalpotentialµisreplacedwheneveritoccursbythelocalquantityµ(r)=µ−V(r)whichincludesthepoten-tialV(r)atpositionrinthetrap.ThisprocedurehasbeenalreadyimplementedattheBCS(mean-field)levelinRef.16,aswellaswiththeinclusionoffluctuationsinRef.17(leadingtotheBogoliubovdescriptionofthecompositebosons).

合集下载

物理学名词

物理学名词

1/4波片quarter-wave plateCG矢量耦合系数Clebsch-Gordan vector coupling coefficient; 简称“CG[矢耦]系数”。

X射线摄谱仪X-ray spectrographX射线衍射X-ray diffractionX射线衍射仪X-ray diffractometer[玻耳兹曼]H定理[Boltzmann] H-theorem[玻耳兹曼]H函数[Boltzmann] H-function[彻]体力body force[冲]击波shock wave[冲]击波前shock front[狄拉克]δ函数[Dirac] δ-function[第二类]拉格朗日方程Lagrange equation[电]极化强度[electric] polarization[反射]镜mirror[光]谱线spectral line[光]谱仪spectrometer[光]照度illuminance[光学]测角计[optical] goniometer[核]同质异能素[nuclear] isomer[化学]平衡常量[chemical] equilibrium constant[基]元电荷elementary charge[激光]散斑speckle[吉布斯]相律[Gibbs] phase rule[可]变形体deformable body[克劳修斯-]克拉珀龙方程[Clausius-] Clapeyron equation[量子]态[quantum] state[麦克斯韦-]玻耳兹曼分布[Maxwell-]Boltzmann distribution[麦克斯韦-]玻耳兹曼统计法[Maxwell-]Boltzmann statistics[普适]气体常量[universal] gas constant[气]泡室bubble chamber[热]对流[heat] convection[热力学]过程[thermodynamic] process[热力学]力[thermodynamic] force[热力学]流[thermodynamic] flux[热力学]循环[thermodynamic] cycle[事件]间隔interval of events[微观粒子]全同性原理identity principle [of microparticles][物]态参量state parameter, state property[相]互作用interaction[相]互作用绘景interaction picture[相]互作用能interaction energy[旋光]糖量计saccharimeter[指]北极north pole, N pole[指]南极south pole, S pole[主]光轴[principal] optical axis[转动]瞬心instantaneous centre [of rotation][转动]瞬轴instantaneous axis [of rotation]t 分布student's t distributiont 检验student's t testＫ俘获K-captureＳ矩阵S-matrixＷＫＢ近似WKB approximationＸ射线X-rayΓ空间Γ-spaceα粒子α-particleα射线α-rayα衰变α-decayβ射线β-rayβ衰变β-decayγ矩阵γ-matrixγ射线γ-rayγ衰变γ-decayλ相变λ-transitionμ空间μ-spaceχ 分布chi square distributionχ 检验chi square test阿贝不变量Abbe invariant阿贝成象原理Abbe principle of image formation阿贝折射计Abbe refractometer阿贝正弦条件Abbe sine condition阿伏伽德罗常量Avogadro constant阿伏伽德罗定律Avogadro law阿基米德原理Archimedes principle阿特伍德机Atwood machine艾里斑Airy disk爱因斯坦-斯莫卢霍夫斯基理论Einstein-Smoluchowski theory 爱因斯坦场方程Einstein field equation爱因斯坦等效原理Einstein equivalence principle爱因斯坦关系Einstein relation爱因斯坦求和约定Einstein summation convention爱因斯坦同步Einstein synchronization爱因斯坦系数Einstein coefficient安[培]匝数ampere-turns安培[分子电流]假说Ampere hypothesis安培定律Ampere law安培环路定理Ampere circuital theorem安培计ammeter安培力Ampere force安培天平Ampere balance昂萨格倒易关系Onsager reciprocal relation凹面光栅concave grating凹面镜concave mirror凹透镜concave lens奥温电桥Owen bridge巴比涅补偿器Babinet compensator巴耳末系Balmer series白光white light摆pendulum板极plate伴线satellite line半波片halfwave plate半波损失half-wave loss半波天线half-wave antenna半导体semiconductor半导体激光器semiconductor laser半衰期half life period半透[明]膜semi-transparent film半影penumbra半周期带half-period zone傍轴近似paraxial approximation傍轴区paraxial region傍轴条件paraxial condition薄膜干涉film interference薄膜光学film optics薄透镜thin lens保守力conservative force保守系conservative system饱和saturation饱和磁化强度saturation magnetization本底background本体瞬心迹polhode本影umbra本征函数eigenfunction本征频率eigenfrequency本征矢[量] eigenvector本征振荡eigen oscillation本征振动eigenvibration本征值eigenvalue本征值方程eigenvalue equation比长仪comparator比荷specific charge; 又称“荷质比(charge-mass ratio)”。

物理玻色-爱因斯坦凝聚(共38张PPT)

物理玻色-爱因斯坦凝聚(共38张PPT)

the condensate.
Einstein predicted that if a gas is cooled to very low temperatures, all the atoms should gather in the lowest energy state. Matter waves of the individual atoms then merge into a single wave; indeed, they can be said to "sing in
图片中部的亮点是一团被俘获的冷却 钠原子。研究者们从1978年开始使 用激光冷却原子，当时最低能够到达 40开尔文。而仅仅十年之后他们就到 达这一记录的百万分之一，该技术的 突飞猛进导致更精确原子钟的产生以 及在极低温下观察到新的超冷物质凝 聚态。
可以用静磁阱来囚禁具有磁偶极矩的中性原子
§4 BEC研究的新进展
知 为T和n的函数。
Predicted 1924.
新领域：非线性原子光学
波长长，频率小，能量小
化学势随温度的降低而升高，当温度降至某一临界温度
Phillips)和斯坦福大学的朱棣文(Steven Chu)首先实现了激光冷却原子的实验，并得到了极低温度(24μK)的钠原子气体。
" Thousands of atoms behave like one big superatom.
玻色-爱因斯坦凝聚
Bose-Einstein Condensation (BEC)
BEC - What is it and where did the idea come from?
BEC in a gas: a new form of matter at the coldest temperatures in the universe...
!!!磁通量量子化实验及超导BCS理论

!!!磁通量量子化实验及超导BCS理论


磁通量量子化实验
由于 0 B0 S 2 ， S 2 为样品2的磁通面积， B0 为 外加场场强。因此前图斜线与上式（*）相符，图 中斜线在纵轴的截距可以看出应是：

hc n 2e
而在横轴的截距正好为：
hc 1 n 2e S 2
磁通量量子化实验
因此，实验又证明了，在未撤去外加磁场 时，超导环仍然维持系统量子化的特性。
BCS理论简介
由于库伯对中电子自旋相反，库伯对的自 旋为零，整体可以看作为一个玻色子。超 导体中的库伯对，可以看作在超导体内的 超流，由玻色-爱因斯坦凝聚解释。
磁通量量子化理论推导
可以认为超导体内载流子的波函数为
为载流子的数密度。 其中 为波函数相位， 根据电磁场中带电粒子的量子理论以及上式可得：
05级量子力学电子作业 刘鹏翃 0510233 二班 物理学
磁通量量子化实验及超导 BCS理论
内容概要
磁通量量子化实验 超导BCS理论简介及磁通量量子化理论推导 超导BCS理论的困难 高温超导材料展望
磁通量量子化实验
1961年由斯坦福大学的B. 迪沃与W. 费尔班 柯完成了超导环内磁通量量子化假设的验 证试验。 其证明了，超导环内的磁通量总是 hc/2e的 整数倍，而非先前伦敦所预言的hc/e。其分 母上电荷量为2e而不是e间接证明了BCS理 论，即超导电流的载流子为库伯电子对， 其电量为2e。
磁通量量子化实验
可以计算，若超导环内存在磁通量量子化效应， 其量子单位：
hc 7 2 2.07 10 gauss cm 2e
为测量此微小磁通量，超导环内的磁通面积应较 小，以使其磁场强在能够人为准确产生与测量的 范围内。
磁通量量子化实验
此实验中，超导环材质为金属锡（Sn）， 其超导转变温度约为3.7K。超导环由在细 铜丝外电镀锡制成，而铜丝直径约为13微 米。 实验中制作了两个超导环样品。 样品1超导锡环内直径为13.3微米,外直径 为2.33微米。 样品2超导锡环内直径为13.5微米，外直径 为16.4微米。
MSEA

MSEA


Author's personal copy
Materials Science and Engineering A 527 (2010) 3245–3252
Contents lists available at ScienceDirect
Materials Science and Engineering A
ห้องสมุดไป่ตู้
scanning electronic microscopy (SEM). The fracture behaviors of the basalt fibers were analyzed from these fractographs. Based on the filament tows model and the statistical theory of fiber strength, a single Weibull statistical model was employed to describe the strength distribution of the basalt filament tows, and the Weibull parameters were obtained by the filament tows testing method. Consistency between the simulated and experimental results indicates that the model and the method are valid and reliable. 2. Experimental 2.1. Basalt fibers The basalt filament tows (as shown in Fig. 1) were manufactured by Hengdian Group Shanghai Russia & Gold Basalt Fiber Co. Ltd. in China. The fineness of the basalt filament tows is 2400tex/21800f (provided by the manufacturer). The diameter of monofilamanet is 7 ␮m. The volume density is 2.6 g/cm3 . The photograph of the bobbin of basalt filament tows is show in Fig. 1. 2.2. Testing The quasi-static tensile tests (with the strain rate of 0.001 s−1 ) and high strain rate tensile tests (impact tensile tests) were performed on a MTS 810.23 materials tester system and a self-designed split Hopkinson tension bar (SHTB) apparatus (as shown in Fig. 2) [12], respectively. The basalt fiber tows were connected with the