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.     

Discrete nature of thermodynamics in confined ideal Fermi gases

Intrinsic discrete nature in thermodynamic properties of Fermi gases appears under strongly confined and degenerate conditions. For a rectangular confinement domain, thermodynamic properties of an ideal Fermi gas are expressed in their exact summation forms. For 1D, 2D and 3D nano domains, variations of both number of particles and internal energy per particle with chemical potential are examined. It is shown that their relation with chemical potential exhibits a discrete nature which allows them to take only some definite values. Furthermore, quasi-irregular oscillatory-like sharp peaks are observed in heat capacity. New nano devices can be developed based on these behaviors.     

强磁场中弱相互作用费米气体的热力学性质

基于赝势法和局域密度近似研究了强磁场中弱相互作用费米气体的热力学性质,得出化学势、总能和热容量的解析式,同时分析了磁场及相互作用对系统热力学性质的影响.研究表明,无论是高温情况还是低温情况下,磁场都能调节相互作用的影响.低温下,与无磁场的系统相比,磁场降低系统的化学势、总能和热容量;与无相互作用系统相比,排斥作用增加化学势而降低总能及热容量.高温下,磁场和排斥作用均可降低系统的总能而增加热容量,强磁场可以改变相互作用对总能及热容量的影响. 关键词： 强磁场 弱相互作用 费米气体 热力学性质     

广义不确定性原理下费米气体低温热力学性质

在考虑到广义不确定性原理时, 统计物理中的态密度必须做出修正, 这导致对传统统计物理的所有结果都有不同程度的修正. 在高能、高温条件下, 此修正是颠覆传统观念的, 在低温条件下, 也有一定的修正. 研究了低温条件下考虑到广义不确定性原理时, 理想费米气体和具有弱相互作用费米气体的热力学性质, 分别给出理想费米气体和弱相互作用费米气体的化学势、内能和定容热容的解析表达式, 并以铜电子气体为例进行了具体数值计算, 将计算结果与不考虑广义不确定性原理时的费米气体的热力学性质进行了比较, 探讨了广义不确定性原理对系统热力学性质的影响. 考虑到广义不确定性原理后费米气体的化学势、费米能和基态能增大, 热容减少, 内能随温度的增加先增大, 到某一温度(对于铜电子气体, T/T_F0～0.3)时, 增值为零, 温度再增加内能减少. 这些修正的具体数值主要由粒子数密度决定, 粒子数密度越大, 修正越大.     

Low-temperature properties of a quantum Fermi gas in curved space-time

We consider the behavior of an ideal quantum Fermi gas in curved space-time. We obtain and analyze the expressions for the densities of the Helmholtz free energy and grand thermodynamic potential in this case. We find the dependence of chemical potential and Fermi energy on the curvature of space-time and compute the explicit expression for the chemical potential of a Fermi gas at high densities and in the low-temperature approximation.     

弱相互作用费米气体的热力学性质

根据赝势法导出无外势时弱相互作用费米气体的化学势、内能和定容热容的解析表达式.在此基础上，采用局域密度近似研究谐振势中弱相互作用费米气体的热力学性质，探讨粒子间相互作用对系统性质的影响. 关键词： 费米气体 相互作用 赝势法 局域密度近似 热力学性质     

The universal sound velocity formula for the strongly interacting unitary Fermi gas

Due to the scale invariance,the thermodynamic laws of strongly interacting limit unitary Fermi gas can be similar to those of non-interacting ideal gas.For example,the virial theorem between pressure and energy density of the ideal gas P=2E/3V is still satisfied by the unitary Fermi gas.This paper analyses the sound velocity of unitary Fermi gases with the quasi-linear approximation.For comparison,the sound velocities for the ideal Boltzmann,Bose and Fermi gas are also given.Quite interestingly,the sound velocity formula for the ideal non-interacting gas is found to be satisfied by the unitary Fermi gas in different temperature regions.     

The performance analysis of a micro-/nanoscaled quantum heat engine

A new model of micro-/nanoscaled heat engines consisting of two thin long tubes with the same length but different sizes of cross section, which are filled up with ideal quantum gases and operated between two heat reservoirs, is put forward. The working fluid of the heat engine cycle goes through four processes, which include two isothermal processes and two isobaric processes with constant longitudinal pressure. General expressions for the power output and efficiency of the cycle are derived, based on the thermodynamic properties of confined ideal quantum gases. The influence of the size effect on the power output and efficiency is discussed. The differences between the heat engines working with the ideal Bose gas and Fermi gas are revealed. The performance of the heat engines operating at weak gas degeneracy and high temperatures is further analyzed. The results obtained are more general and significant than those in the current literature.     

弱磁场中弱相互作用费米气体的热力学性质

根据赝势法和系综理论导出弱磁场中弱相互作用费米气体的内能、化学势和热容量的小参数r的解析式.在此基础上给出高温和低温两种情况下弱磁场中弱相互作用费米气体的热力学性质,探讨磁场及粒子间相互作用对热力学性质的影响,分析磁场与三维谐振势两种约束对系统性质影响的不同及其原因. 关键词： 赝势法 费米气体 相互作用 热力学性质     

Parametric optimum analysis of an irreversible Ericsson cryogenic refrigeration cycle working with an ideal Fermi gas

An irreversible model of an Ericsson cryogenic refrigeration cycle working with an ideal Fermi gas is established, which is composed of two isothermal and two isobaric processes. The influence of both the quantum degeneracy and the finite-rate heat transfer between the working fluid and the heat reservoirs on the performance of the cycle is investigated, based on the theory of statistical mechanics and thermodynamic properties of an ideal Fermi gas. The inherent regeneration losses of the cycle are analyzed. Expressions for several important performance parameters such as the coefficient of performance, cooling rate and power input are derived. By using numerical solutions, the cooling rate of the cycle is optimized for a given power input. The maximum cooling rate and the corresponding parameters are calculated numerically. The optimal regions of the coefficient of performance and power input are determined. Especially, the optimal performance of the cycle in the strong and weak gas degeneracy cases and the high temperature limit is discussed in detail. The analytic expressions of some optimized parameters are derived. Some optimum criteria are given. The distinctions and connections between the Ericsson refrigeration cycles working with the Fermi and classical gases are revealed.      

金属中自由电子气体的非广延统计研究

采用分解近似的方法讨论了在Tsallis量子统计物理框架中，金属中自由电子气体的非广延参数q的热力学统计处理，计算出了总粒子数、总能量、自由能、热容量等热力学量，得出结论：在低温区域，q→1时，所有结果都可以回到传统的Fermi-Dirac分布，非广延参数q控制着系统的非广延程度.最后，详细讨论了q与热容量之间的关系，并与以前的结果作了比较. 关键词： Tsallis广义统计 非广延参数q 自由电子气体 Fermi-Dirac分布     

Thermodynamics of boson and fermion systems with fractal distribution functions

Starting with the fractal-inspired distribution functions for Maxwell-Boltzmann, Bose-Einstein, and Fermi systems, as reported by Büyükkili? and Demirhan, we obtain the corresponding probability distributions and study their thermodynamic behavior. We compare our results with those corresponding to ideal gases (q=1) and Bose-Einstein and Fermi systems with quantum group symmetry. In particular, we show that the Hamiltonian that gives the Bose-Einstein generalized distribution function can be interpreted as a q deformation of the ideal gas Hamiltonian.     

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.     

重力场和强磁场中费米气体的热力学性质

基于半经典近似,研究重力场和强磁场共存下费米气体的热力学性质,通过理论解析和数值模拟分析强磁场背景下重力场对系统热力学性质的影响.研究表明:与单纯强磁场相比,重力场的引入使能量及化学势都降低.随温度的上升,重力场对化学势的影响逐渐放大;对热容的影响有极大值.重力场使系统的热容随磁场的振荡几乎不变、使化学势的振荡中心下移.     

磁场中非广延相对论费米系统的统计性质

基于广义外势中的非广延统计理论,运用理论解析与数值模拟方法,研究磁场中非广延极端相对论费米气体的热力学性质,给出总能、热容量、化学势的解析式,分析非广延参数、极端相对论效应、磁场及温度对系统热力学性质的影响机理.研究显示,非广延参数不仅对热力学性质有直接的影响,而且也影响着磁场的物理效应. 随温度的升高,非广延参数及磁场对热力学性质的影响均被放大.极端相对论效应对化学势及热容量有特别显著的影响.     

Effects of boundaries on the thermodynamic properties of a Fermi gas

The discussion concerns an ideal gas bounded by an impermeable rough surface. The density of states is calculated for various limiting cases and is averaged for randomly distributed roughness. The changes in some thermodynamic parameters due to this surface are calculated for a highly degenerate Fermi gas.     

Pauli Paramagnetic Susceptibility of an Ideal Anyon Gas within Haldane Fractional Exclusion Statistics

The finite-temperature Pauli paramagnetic susceptibility of a three-dimensional ideal anyon gas obeying Haldane fractional exclusion statistics is studied analytically.Different from the result of an ideal Fermi gas,the susceptibility of an ideal anyon gas depends on a statistical factor g in Haldane statistics model.The low-temperature and high-temperature behaviors of the susceptibility are investigated in detail.The Pauli paramagnetic susceptibility of the two-dimensional ideal anyons is also derived.It is found that the reciprocal of the susceptibility has the similar factorizable property which is exhibited in some thermodynamic quantities in two dimensions.     

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.     

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.     

The simple fundamental equation of state for liquid,gas, and fluid of xenon

To describe the thermodynamic properties of xenon, a new fundamental low-parametric equation of state (in the form of reduced Helmholtz energy) is obtained with the help of the methods and approaches developed by the authors. It allows us to describe the thermal properties of gas, liquid, and fluid with a sufficiently high accuracy close to the accuracy of experiment in a range from the density in the ideal gas state to the density at the triple point, excluding the critical region. The caloric properties and speed of xenon sound are calculated without involving any caloric data, with the exception of ideal gas enthalpy. The values of isobaric heat capacity, sound speed, and other thermodynamic properties obtained by calculations are in good agreement with the experimental data.