Free energy of gravitating fermions

We calculate rigorously, in a suitable thermodynamic limit, the free energy of a system of nonrelativistic fermions which interact with attractiver ^–1-potentials. It is shown that the effective field approximation becomes exact in this limit and results in the temperature-dependent Thomas-Fermi equations.On leave of absence from the University of Heidelberg, Germany.On leave of absence from the University of Vienna, Austria.     

Thermodynamic functions for fermions with gravostatic and electrostatic interactions

The energy as function of entropy and the free energy as function of temperature is calculated rigorously for nonrelativistic fermions with interactions. It is shown that in the appropriate thermodynamic limit the corresponding Thomas-Fermi equation becomes exact.Work supported by Fonds zur Förderung der wissenschaftlichen Forschung, Projekt Nr. 1391.On leave of absence from the University of Heidelberg, Germany.     

Thermodynamic equilibrium of a gravitating sphere in Lyra's geometry

This paper deals with a particular case of Lyra's modification of Riemannian geometry in which the consequences of the thermodynamic equilibrium of a gravitating fluid sphere have been considered. These considerations lead to a zero red shift in this static model.     

Thermodynamic limit for a system with dipole-dipole interactions

The free energy at constant magnetization of a simple cubic lattice of Ising spins with dipole-dipole interactions in periodic boundary conditions is related to the free energy at constant magnetization with no periodicity. The relationship is not one of equality.     

Equilibrium time correlation functions in the low-density limit

We consider a system of hard spheres in thermal equilibrium. Using Lanford's result about the convergence of the solutions of the BBGKY hierarchy to the solutions of the Boltzmann hierarchy, we show that in the low-density limit (Boltzmann-Grad limit): (i) the total time correlation function is governed by the linearized Boltzmann equation (proved to be valid for short times), (ii) the self time correlation function, equivalently the distribution of a tagged particle in an equilibrium fluid, is governed by the Rayleigh-Boltzmann equation (proved to be valid for all times). In the latter case the fluid (not including the tagged particle) is to zeroth order in thermal equilibrium and to first order its distribution is governed by a combination of the Rayleigh-Boltzmann equation and the linearized Boltzmann equation (proved to be valid for short times).Supported in part by NSF Grant PHY 78-22302.     

Thermodynamic stability of interacting fermions system with matrix eigenvalue method

A matrix eigenvalue method is applied to analyse the thermodynamic stability of two-component interacting fermions. The non-relativistic and ultra-relativistic d=1, 2,3 dimensions have been discussed in detail, respectively. The corresponding stability region has been given according to the two-body interaction strength and the particle number density ratio.     

The classical limit for quantum mechanical correlation functions

For quantum systems of finitely many particles as well as for boson quantum field theories, the classical limit of the expectation values of products of Weyl operators, translated in time by the quantum mechanical Hamiltonian and taken in coherent states centered inx- andp-space around? ^?1/2 (coordinates of a point in classical phase space) are shown to become the exponentials of coordinate functions of the classical orbit in phase space. In the same sense,? ^?1/2 [(quantum operator) (t) — (classical function) (t)] converges to the solution of the linear quantum mechanical system, which is obtained by linearizing the non-linear Heisenberg equations of motion around the classical orbit.     

Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics

We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge and the horizon radius. These scale transformations form a one-parameter multiplicative group, leading to universal “renormalization group”-like first-order differential equations. The beams of characteristics of these equations generate the full set of black hole states associated to any of these gravitating nonlinear electrodynamics. Moreover the application of the scaling laws allows to find a universal finite relation between the thermodynamic variables, which is seen as a generalized Smarr law. Some particular well known (and also other new) models are analyzed as illustrative examples of these procedures.     

Time correlation functions of a one-dimensional infinite system

We investigate the time evolution of a simple one-dimensional system with an infinite number of particles. We calculate some time correlation functions and show that they behave asymptotically as 1/t.     

Simple relations between correlation functions in a closed system

From conservation of total momentum of a general closed system relations between certain correlation functions are derived. The procedure is then applied to express the electrical conductivity of an arbitrary solid or liquid by the dynamics of its nuclei. The possibility to get the wanted information about nuclear motion from inelastic thermal neutron scattering is discussed. For a solid the dynamics of the nuclei are calculated in the harmonic approximation.     

Thermodynamic limit in a charged plasma in equilibrium

We study the existence conditions for the thermodynamic limit in the chain of BBGKY equations for the equilibrium correlation functions of a charged plasma. It is shown that in order for the thermodynamic limit to exist the charge of the plasma cannot increase faster than the surface area of the plasma. When this condition is satisfied the equilibrium correlation functions of the charged plasma are asymptotically identical to the correlation functions of a neutral plasma in a self-consistent electrostatic field, which depends only on the one-particle correlation functions. For a plasma which is uniform everywhere except in a thin surface region, this field is found in explicit form. For a plasma occupying an infinite half-space, the problem is equivalent to a neutral plasma near a charged wall.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, 11–16, February, 1987.     

Nonstandard mixing in a system of fermions

In this paper we continue to study the mixing of fermionic fields with different parities. Here we are interested in the manifestation of the latter in pion-nucleon scattering, which is analyzed for systems with particles having 3/2^± spins. Also, theoretical calculations are compared with experimental data from the partial analysis.     

受限一维无自旋费米子系统的性质研究

本文借助于一维自旋1/2-XXZ模型的Bethe-ansatz精确解, 利用局域密度近似(LDA), 讨论了谐振势中一维无自旋费米子的密度分布, 得出了ρ-u相图(这里的ρ为无量纲的粒子数密度 变量u为相互作用强度)对相图的分析表明, 随着原子密度和近邻相互作用的变化, 系统出现五个不同的混合量子相通过对热力学硬度S_ρ的计算, 发现其可作为体系的序参量, 其奇异点可用以度量受限体系中量子相变的发生     

Thermodynamic functions of a spin glass

We have measured the specific heats of several dilute ZnMn alloys, and from these results have found simple analytic expressions for the free energy, internal energy, entropy and specific heat of this typical spin glass alloy.     

A scalar-fermion model in the limit of infinitely heavy fermions

As a first step in the non-perturbative study of a chiralU(1)?U(1) Yukawa-model with explicit mirror fermions the limit of infinite bare fermion mass is considered. Non-perturbative information is obtained from 14th order scalar hopping parameter expansion, which is confronted with high statistics numerical data. A remarkable universality of the upper bound for the renormalized quartic coupling is observed. A new kind of first order phase transition surface is localized, which is characterized by a large jump in the average field length.     

Relaxation and lyapunov time scales in a one-dimensional gravitating sheet system

The relation between relaxation, the time scale of Lyapunov instabilities, and the Kolmogorov-Sinai time in a one-dimensional gravitating sheet system is studied. Both the maximum Lyapunov exponent and the Kolmogorov-Sinai entropy decrease as proportional to N(-1/5). The time scales determined by these quantities evidently differ from any type of relaxation time found in the previous investigations. The relaxation time to quasiequilibria (microscopic relaxation) is found to have the same N dependence as the inverse of the minimum positive Lyapunov exponent. The relaxation time to the final thermal equilibrium differs from the inverse of the Lyapunov exponents and the Kolmogorov-Sinai time.     

Trapped fermions with density imbalance in the Bose-Einstein condensate limit

We analyze the effects of imbalancing the populations of two-component trapped fermions, in the Bose-Einstein condensate limit of the attractive interaction between different fermions. Starting from the gap equation with two fermionic chemical potentials, we derive a set of coupled equations that describe composite bosons and excess fermions. We include in these equations the processes leading to the correct dimer-dimer and dimer-fermion scattering lengths. The coupled equations are then solved in the Thomas-Fermi approximation to obtain the density profiles for composite bosons and excess fermions, which are relevant to the recent experiments with trapped fermionic atoms.