简谐势阱中理想Fermi气体的有限尺度效应（英文）

在定义特征长度的基础上,应用Euler–MacLaurin公式,研究了三维简谐势阱中有限理想Fermi气体的热力学性质.给出了具有有限尺度效应修正的化学势、内能、压强张量与状态方程和热容量的解析表达式,分别就强简并和弱简并的情况进行了讨论.揭示了简谐势阱中有限尺度效应的实质以及与处于D维容器中的不同,指出了简谐势阱中的有限尺度效应使得热力学量减小,压强的各向同性(或各向异性)取决于简谐势的各向同性(或各向异性),T=0K时费米能和基态内能在满足一定边界条件时分别存在一个极大值.     

有限尺度下弱相互作用费米气体的热力学性质

基于巨正则系综理论和数值模拟方法,研究有限尺度下弱相互作用费米气体的热力学性质,给出系统低温下的化学势、能量及热容量的解析式,分析弱相互作用、有限尺度效应对系统热力学性质的影响.研究表明,有限尺度和排斥相互作用增大了系统的化学势、能量,吸引相互作用减小了系统的化学势、能量.相互作用受到尺度的调制,尺度变大,相互作用影响变小,相互作用和尺度效应都受到温度的调制,温度升高,相互作用和尺度的影响减小.尺度和相互作用的一级修正对热容量无影响.     

以理想费米气体为工质的量子制冷循环

本文基于理想费米气体的状态方程，分析了以理想费米气体为工质的量子Ericsson制冷循环中的回热特征，推导出其制冷循环的制冷系数表达式。并在高温和低温条件下对制冷系数进行了讨论。这将对低温制冷机的研究提供理论依据。     

理想玻色气体的焦汤系数

应用玻色系统的基本方程，玻色积分的特性以及热力学理论，导得理想玻色气体焦汤系数的解析表达式，详细讨论了低温下玻色气体的定压热容和焦汤系数，阐明了系统的量子本性对焦汤系数的贡献，表明理想玻色气体适用于低温制冷系统。     

一维谐振子势阱中的理想量子气体

本文利用微正则系综研究了囚禁于一维谐振子势阱中的无相互作用的玻色气体和费米气体的热力学性质,并指出一维谐振子势阱中理想玻色气体和费米气体的热力学性质是相同的.     

弱磁场中弱相互作用费米气体的有限粒子数效应(英文)

由弱磁场中弱相互作用费米气体的配分函数,导出有限粒子数条件下系统的配分函数G(β,N ).在此基础上,运用统计平均方法求解有限粒子数弱相互作用费米气体热力学量的解析表达式,给出各种温度条件下的热力学性质.研究结果表明,有限粒子数效应使各个热力学量都产生了一个修正项,除温度趋于0外,粒子数对化学势的修正项有直接影响,对内能和热容量的修正项并不产生直接影响.并且有限粒子数效应总是降低化学势,从而使化学势的0点向低温漂移,粒子数增大,会削弱这种效应,粒子间的相互排斥会加强这种效应.     

硬球势中相对论费米气体的热力学性质

用量子统计与数值模拟相结合的方法,在广义外势中相对论费米系统的热力学量的基础上,研究硬球势中相对论费米气体的热力学性质.得到了考虑相对论效应时系统的内能和热容量的解析表达式,分析了相对论效应对内能和热容量的影响.研究表明:与非相对论比较,相对论费米气体的内能和热容量更高;相对论特征量越大,热容量的转折温度越低;随着温度的升高,特征量越大,内能就越大.     

有限尺度下弱相互作用费米气体的热力学性质

基于巨正则系综理论和数值模拟方法,研究有限尺度下弱相互作用费米气体的热力学性质,给出系统低温下的化学势、能量及热容量的解析式,分析弱相互作用、有限尺度效应对系统热力学性质的影响.研究表明,有限尺度和排斥相互作用增大了系统的化学势、能量,吸引相互作用减小了系统的化学势、能量.相互作用受到尺度的调制,尺度变大,相互作用影响变小,相互作用和尺度效应都受到温度的调制,温度升高,相互作用和尺度的影响减小.尺度和相互作用的一级修正对热容量无影响.     

极高压强下气体的性质

气体在极高压强下不再遵从玻意耳定律和盖·吕萨克定律，而代之以 Ｌｅｖｉｔｔ建议的两个经验公式 ｐ＝ ＣｅＢ／Ｖ及＝Ｖ０＋αｐＴ．根据这两个经验公式，我们计算了在极高压强下气体的各种热力学性质，讨论了它们随压强和温度的变化趋势，并且与理想气体和范德瓦耳斯气体的情形进行了比较     

量子点中的近藤效应

大块稀磁合金的电阻作为温度的函数在低温下具有一个极小值．１９６４年，近藤从理论上阐明了磁性杂质对传导电子的散射几率随温度下降而增大的起因，“近藤效应”因此而得名．然而，对于量子点，其中与磁性相关的低温输运行为（近藤效应）却表现出许多新特点．在ＧａＡｓ...     

Finite-size effects in a D-dimensional ideal Fermi gas

By using the Euler-MacLaurin formula,this paper studies the thermodynamic properties of an ideal Fermi gas confined in a D-dimensional rectangular container.The general expressions of the thermodynamic quantities with the finite-size corrections are given explicitly and the effects of the size and shape of the container on the properties of the system are discussed.It is shown that the corrections of the thermodynamic quantities due to the finite-size effects are significant to be considered for the case of strong degeneracy but negligible for the case of weak degeneracy or non-degeneracy.It is important to find that some familiar conclusions under the thermodynamic limit are no longer valid for the finite-size systems and there are some novel characteristics resulting from the finite-size effects,such as the nonextensivity of the system,the anisotropy of the pressure,and so on.     

Finite-size effect and Kondo screening effect in an A-B ring with a quantum dot

The properties of the ground state of a closed dot－ring system with a magnetic flux in the Kondo regime are studied theoretically by means of a one-impurity Anderson Hamiltonian. The Hamiltonian is solved by means of the slave-boson mean-field theory. It is shown that at T=0, a suppressed Kondo effect exists in this system even when the mean level spacing of electrons in the ring is larger than the bulk Kondo temperature. The physical quantities depend sensitively on both the parity of the system and the size of the ring; the rich physical behaviour can be attributed to the coexistence of both the finite-size effect and the Kondo screening effect. It is also possible to detect the Kondo screening cloud by measuring the persistent current or the zero field impurity susceptibility χ_{imp} directly in future experiments.     

理想气体在热力学中的作用

指出热力学理论是普遍的,不依赖于理想气体.理想气体为热力学理论提供了一个简单的实例,为测量热力学温度提供了一种简单的温度计.     

Thermodynamic coefficients of ideal Fermi gas

We present analytical formulae for the first and second derivatives of the Helmholtz free energy of non-relativistic ideal Fermi gas. Important thermodynamic quantities such as heat capacity, sound velocity, heat capacity ratio, and others are explicitly expressed through the derivatives. We demonstrate correct ideal Boltzmann gas and low-temperature Fermi gas asymptotes and derive corrections to thermodynamic functions for these limiting cases. Numerical computations of thermodynamic properties of ideal Fermi gas can be accurately performed using the developed freely available Python module ifg .     

理想气体任意过程最高和最低温度的计算方法

给出理想气体任意过程最高和最低温度的三种计算方法，用p-V图中的直线过程、圆过程、椭圆过程为例，计算该过程最高、最低温度的状态。     

Spin interaction with an ideal Fermi gas

We consider the equilibrium dynamics of a system consisting of a spin interacting with an ideal Fermi gas on the lattice , 3. We present two examples: when this system is unitarily equivalent to an ideal Fermi gas or to a spin in an ideal Fermi gas without interaction between them.     

Mesoscopic effects in the quantum Hall regime

We report results of a study of (integer) quantum Hall transitions in a single or multiple Landau levels for non-interacting electrons in disordered two-dimensional systems, obtained by projecting a tight-binding Hamiltonian to the corresponding magnetic subbands. In finite-size systems, we find that mesoscopic effects often dominate, leading to apparent non-universal scaling behavior in higher Landau levels. This is because localization length, which grows exponentially with Landau level index, exceeds the system sizes amenable to the numerical study at present. When band mixing between multiple Landau levels is present, mesoscopic effects cause a crossover from a sequence of quantum Hall transitions for weak disorder to classical behavior for strong disorder. This behavior may be of relevance to experimentally observed transitions between quantum Hall states and the insulating phase at low magnetic fields.     

On the derivation of the entropy of ideal quantum gases confined in a three-dimensional harmonic potential

In this work,the entropy functions of ideal quantum gases in a three-dimensional harmonic trap are analytically calculated using temperature as an explicit variable.Afterward,the applicability of the analytical formulas is validated by comparison with the numerical calculation.The results illustrate that the obtained functions could be applied for the whole temperature regime with a maximum relative deviation of less than 7.5%in the vicinity of the critical temperature Tcin the case of Bose gases.Meanwhile,for Fermi gases,although the analytical formula fits well at very low-and high-temperature regimes,it cannot be applied at temperature in the range[0.3-0.5]T_F,where T_F is the Fermi temperature.In addition,the consistency between our formulas and classical ones at significantly high temperatures is also discussed.     

Finite-size scaling for correlations of quantum spin chains at criticality

We study the finite-size scaling behavior of two-point correlation functions of translationally invariant many-body systems at criticality. We propose an efficient method for calculating the two-point correlation functions in the thermodynamic limit from numerical data of finite systems. Our method is most effective when applied to a two-dimensional (classical) system which possesses a conformal invariance. By using this method with numerical data obtained from exact diagonalizations and Monte Carlo simulations, we study the spin-spin correlations of the quantum spin-1/2 and-3/2 antifierromagnetic chains. In particular, the logarithmic corrections to power-law decay of the correlation of the spin-1/2 isotropic Heisenberg antiferromagnetic chain are studied thoroughly. We clarify the cause of the discrepancy in previous calculations for the logarithmic corrections. Our result strongly supports the field-theoretic prediction based on the mappings to the Wess-Zumino-Witten nonlinear -model or the sine-Gordon model. We also treat logarithmic corrections and crossover phenomena in the spin-spin correlation of the spin-3/2 isotropic Heisenberg antiferromagnetic chain. Our results are consistent with the Affleck-Haldane prediction that the correlation of the spin-3/2 chain exhibits a crossover to the same asymptotic behavior as in the spin-1/2 chain.