简谐势阱中旋转费米气体的热力学性质  

Thermodynamics of Rotating Fermi Gases in a Harmonic Trap

作　　者：刘红艳 李玉山 LIU Hong-yan;LI Yu-shan(School of Physics and Electronic Engineering,Heze University,Heze 274015,China)

机构地区：[1]菏泽学院物理与电子工程学院,山东菏泽274015

出　　处：《量子光学学报》2021年第4期295-301,共7页Journal of Quantum Optics

基　　金：国家自然科学基金项目(11804085);山东省自然科学基金项目(ZR2017MEM012)。

摘　　要：利用局域密度近似建立了简谐势阱中存在相互作用的旋转费米气体的粒子数密度、化学势、内能、热容量和粒子流密度的解析表达式,讨论了粒子间相互作用的影响。结果表明:势阱和吸引相互作用趋于约束粒子在势阱中心附近,而旋转和排斥相互作用则使势阱中心区域粒子密度和流密度均有所减小。费米面附近的量子态强烈影响费米子流密度的振荡行为,对振荡起主导作用。排斥相互作用使化学势和总能比无互作用费米系统略大,而吸引相互作用则使化学势和总能比无互作用费米系统有所减小。相互作用对热容量的影响则在不同温区呈现出完全不同的特征。当相互作用消失时,所有解析结果均能够与旋转理想费米气体获得一致。Analytical expressions of the particle number density,chemical potential,total energy,specific heat and the spatial distribution of particle current density for rotating interacting Fermi gases in a harmonic trap are derived based on the local density approximation(LDA).The effect of mutual interaction between the nearby atoms plays an important impact on the thermodynamics.Especially,the spatial distribution of current density is discussed in detail.The results show that the centrifugal force caused by rotation is always competing with the binding force confined by the harmonic trap.The harmonic trap and attractive interaction tend to concentrate the particles around the center of the trap.The rotation and repulsive interaction tend to decentralize the particles away from the center,which decreases the particle number density and particle current density.Their mutual competition results in the particle distribution being more scattered.Moreover,two sharp and opposite oscillations appear in the spatial distribution of fermion current density.The numerical results indicate that the amplitude and period of oscillations in the spatial distribution of fermion current density are strongly affected by the quantum states near the Fermi surface,which play a dominant contribution to these oscillations.Compared with the case of the ideal Fermi system,the repulsive interaction increases the chemical potential and total energy while the attractive interaction decreases them.The influence of mutual interaction on the specific heat shows completely different characteristics at various temperatures.At the low temperature,repulsive(attractive)interaction makes the heat capacity larger(smaller).At the high temperature,repulsive(attractive)interaction makes the heat capacity smaller(larger)and finally tends to a constant.The results given in this paper can be treated as the general reference for the multiscale analysis of rotating ideal Fermi gases and the other Fermi system.When the mutual interaction disappears,these results com

关 键 词：费米流密度 简谐势阱 热力学性质 

分 类 号：O469[理学—凝聚态物理]