Equation of state for agents on graphs

Based on the generalized statistic distribution derived from the Tsallis entropy that has been successfully used in complex systems with long-range interactions and/or long-duration memory, the thermostatistic properties of a q-generalized Fermi system are studied. The total number of particles, internal energy, and heat capacity at constant volume are calculated for two different cases of q1 and q1, respectively, where q is an important parameter to evaluate the nonextensivity of the system. The thermostatistic characteristics of the system are discussed in detail. It is found from the results obtained here that the Fermi energy of such a system is independent of the parameter q and is equal to that of an original ideal Fermi system when q1, while other thermostatistic properties of the system depend closely on the parameter q. For example, when q<1, the chemical potential of the system in certain region of temperature may be larger than the Fermi energy; when q>1, some thermodynamic parameters of the system at low temperatures must be cut off.     

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     

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.     

Thermodynamics of two-parameter quantum group Bose and Fermi gases

The high and low temperature thermodynamical properties of the two-parameter deformed quantum group Bose and Fermi gases with SU _p/q (2) symmetry are studied. Starting with a SU _p/q (2)-invariant bosonic as well as fermionic Hamiltonian, several thermodynamical functions of the system such as the average number of particles, internal energy and equation of state are derived. The effects of two real independent deformation parameters p and q on the properties of the systems are discussed. Particular emphasis is given to a discussion of the Bose-Einstein condensation phenomenon for the two-parameter deformed quantum group Bose gas. The results are also compared with earlier undeformed and one-parameter deformed versions of Bose and Fermi gas models. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

A unified grand canonical description of the nonextensive thermostatistics of the quantum gases: Fractal and fractional approach

In this paper, the particles of quantum gases, that is, bosons and fermions are regarded as g-ons which obey fractional exclusion statistics. With this point of departure the thermostatistical relations concerning the Bose and Fermi systems are unified under the g-on formulation where a fractal approach is adopted. The fractal inspired entropy, the partition function, distribution function, the thermodynamics potential and the total number of g-ons have been found for a grand canonical g-on system. It is shown that from the g-on formulation; by a suitable choice of the parameters of the nonextensivity q, the parameter of the fractional exclusion statistics g, nonextensive Tsallis as well as extensive (q=1) standard thermostatistical relations of the Bose and Fermi systems are recovered. Received 17 September 1999     

Harmonically trapped jellium

We discuss the model of a D-dimensional confined electron gas in which the particles are trapped by a harmonic potential. In particular, we study the non-interacting kinetic and exchange energies of finite-size inhomogeneous systems, and compare the resulting Thomas–Fermi and Dirac coefficients with various uniform electron gas paradigms. We show that, in the thermodynamic limit, the properties of this model are identical to those of the D-dimensional Fermi gas.     

A parabolic quantum dot with N electrons and an impurity

Ground-state properties of a two-dimensional quantum dot composed of N electrons and an impurity are investigated by the Thomas–Fermi (TF) method at T=0. The changes induced by the impurity in electron density, chemical potential and total energy are calculated. Calculations are also performed for different number of particles and strength of confinement. The results indicate that Thomas–Fermi approximation is applicable even when the system contains only a few particles.     

Fermi气体在势阱中的最大囚禁范围与状态方程

在Thomas-Fermi近似条件下,研究了n维广义幂律势阱中Fermi原子气体的最大囚禁范围,给出了n维势阱中气体的实际囚禁体积,导出了状态方程.结果表明,最大囚禁范围和囚禁气体压强不仅与势阱性质有关,也与自由理想Fermi系统的化学势有关.对三维球对称简谐势阱进行了应用,表明在Thomas-Fermi近似有效的前提下,当系统满足条件((kT)/(hω))² ((16π²g)/ 关键词： Fermi气体 n维势阱')" href="#">n维势阱 最大囚禁范围 状态方程     

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.     

实际费米气体的低温性质

实际气体粒子间都存在弱的相互作用,利用赝势法求出无外势时实际费米气体的能谱,导出了低温低密度下实际费米气体的化学势、压强、熵、内能和定容热容等物理量的解析表达式,探讨了粒子间相互作用对系统低温性质的影响．     

Dynamical Properties of the Unitary Fermi Gas: Collective Modes and Shock Waves

We discuss the unitary Fermi gas made of dilute and ultracold atoms with an infinite s-wave inter-atomic scattering length. First we introduce an efficient Thomas–Fermi–von Weizsacker density functional which describes accurately various static properties of the unitary Fermi gas trapped by an external potential. Then, the sound velocity and the collective frequencies of oscillations in a harmonic trap are derived from extended superfluid hydrodynamic equations which are the Euler–Lagrange equations of a Thomas–Fermi–von Weizsacker action functional. Finally, we show that this amazing Fermi gas supports supersonic and subsonic shock waves.     

Thermodynamics of trapped fermions in gravitational field

Trapped non-interacting Fermi gas in an external gravitational field in Newtonian approximation is considered. Analytical equations for the internal energy, the number of particles are computed. The analytical expression for the specific heat of trapped Fermi gas in non-homogeneous gravitational field is found.     

Ultracold finite-size Fermi gas in a quartic trap

Low temperature properties of a finite-size ideal Fermi gas trapped in a quartic potential are studied. The curves of the chemical potential and specific heat varying with the particle number and temperature are plotted. The results obtained here are based on the numerical calculation of the state sum without invoking the Thomas–Fermi approximation, so that the more detailed dependences of the chemical potential and specific heat on the particle number and temperature are revealed.     

Finite Fermi systems theory and self-consistency relations

The self-consistent theory of the finite Fermi systems is outlined. This approach is based on the same Fermi liquid theory principles as the familiar theory for finite Fermi systems (FFS) by Migdal. We show that the basic Fermi system properties can be evaluated in terms of the quasiparticle Lagrangian L_q which incorporates the energy dependency effects. This Lagrangian is defined so that the corresponding Lagrange equations should coincide with the FFS theory equations of motion of the quasiparticles. The quasiparticle energy E_q defined in the terms of t he quasiparticle Lagrangian L_q according to the usual canonical rules is shown to be equal to the binding energy E_o of the system. For a given Lagrangian L_q the particle densities in nuclei, the nuclear single-particle spectra, the low-lying collective states (LCS) properties, and the amplitude of the interquasiparticle interaction are also evaluated. The suggested approach is compared with the Hartree-Fock theory with effective forces.     

Thermodynamic stability of a weakly interactingFermi gas trapped in a harmonic potential

Based on the theoretical results derived from pseudopotential method and local approximation, this paper studies the thermodynamic stability of a weakly interacting Fermi gas trapped in a harmonic potential by using analytical method of thermodynamics. The effects of the interparticle interactions as well as external potential on the thermodynamic stability of the system are discussed. It is shown that the system is stable as for the complete average, but as for local parts, the system is unstable anywhere. This instability shows that the stability conditions of mechanics cannot be satisfied anywhere, and the stability conditions of thermostatics cannot be satisfied somewhere. In addition, the interactions and external potential have direct effects on the local stability of the system.     

A microscopic study of the finite two-dimensional trapped bose atomic gas

Using the static fluctuation approximation, finite two-dimensional Bose gas systems, trapped in a harmonic potential, are investigated. The interparticle potential is taken as a δ-function. The chemical potential, condensate fraction, total energy, and heat capacity are calculated as functions of the temperature for different values of the interaction strength and of the number of particles. Our results show that interacting bosons trapped in a harmonic potential have a similar behavior to that of the ideal system. These results conform with those obtained using different many-body theories, such as the semi-classical two-fluid model and the Hartree–Fock approximation.     

Pulse duration effects on laser-assisted electron transfer cross section for He2+ ions colliding with atomic hydrogen

The physics of a two-component cold Fermi gas is now frequently addressed in laboratories. Usually this is done for large samples of tens to hundreds of thousands of particles. However, it is now possible to produce few-body systems (1–100 particles) in very tight traps where the shell structure of the external potential becomes important. A system of two-species fermionic cold atoms with an attractive zero-range interaction is analogous to a simple model of nucleus in which neutrons and protons interact only through a residual pairing interaction. In this article, we discuss how the problem of a two-component atomic Fermi gas in a tight external trap can be mapped to the nuclear shell-model so that readily available many-body techniques in nuclear physics, such as the Shell-Model Monte Carlo (SMMC) method, can be directly applied to the study of these systems. We demonstrate an application of the SMMC method by estimating the pairing correlations in a small two-component Fermi system with moderate-to-strong short-range two-body interactions in a three-dimensional harmonic external trapping potential.     

Quantum states and Fermi surfaces in metals with an fcc lattice in an ultrastrong magnetic field

The expression for the electron wave function for a 3D crystal in a constant magnetic field is obtained in the strong coupling approximation. A 3D Harper-type equation describing the electron spectrum in magnetic 3D subbands is derived. The Fermi surfaces for monovalent noble metals are constructed for various orientations and magnitudes of magnetic fields corresponding to a rational number p/q of the magnetic flux quanta; radical changes in the topology of the Fermi surfaces in a strong magnetic field are observed. As a result, considerable changes in the physical properties of crystals in a strong magnetic field can be expected. In particular, a metal-semiconductor transition occurs for all even values of q, while metallic properties are preserved for odd values of q. The total energy of electrons as a function of the magnetic field is also calculated and shows a minimum for p/q=1/2. The type of thermodynamic oscillations in an ultrastrong magnetic field is discussed. The effects considered by the authors may be observed in fields with a strength of several tens of megagausses.     

由N-E-V分布及赝势法研究弱磁场中弱相互作用费米子气体的热力学性质

基于低温下量子系统的相关实验多是在体积、能量和粒子数都可变的外场束缚下进行的事实, 由体积、能量和粒子数可变的完全开放系统的统计分布(N-E-V分布)研究了弱磁场中弱相互作用费米系统的热力学性质. 首先求出了一般情况下由费米积分表示的内能和热容的解析表达式. 在此基础上, 又给出了在低温极限条件下内能与热容的解析表达式和数值计算结果, 并将N-E-V分布(粒子数密度变化)的结果与赝势法(粒子数密度不变)的结果进行了比较. 结果表明: N-E-V分布方法的计算结果总是补偿赝势法计算结果的过度偏差. 由N-E-V 分布方法所得结果最特异之处在于: 在低温条件下, 弱磁场中弱相互作用费米系统存在一相变温度t_c, 其正处于费米系统发生玻色-爱因斯坦凝聚(BEC)和费米原子形成库珀对的超流状态(BCS)相变及BEC-BCS跨越的温度范围内, 且不随反映弱相互作用大小和特征的散射长度a (a<0引力, a>0斥力)变化, 但随弱磁场的加强而降低, 即弱磁场可调节该相变温度. 磁场为零时, 相变温度最高, 为费米温度的0.184倍.