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Acta Physica Sinica

The influence of weak interaction on thermodynamic properties and the stability of imperfect Bose gas

Yuan Du-Qi, 宝鸡文理学院物理系，宝鸡 721007

Published Jan 1, 2006• 4 citations
Publisher

Abstract

Using the free energy and the equation of state for an imperfect Bose gas, the analytical expression between the critical temperature and the length of dispersion wave and the pressure for the imperfect Bose gas is derived. The unusual properties of the specific heat at constant pressure and the expansion coefficient at constant pressure and isothermal compressibility by the attractive force for the imperfect Bose gas are revealed. The instability arising from the attractive force is pointed out, and the temperature criterion and particle density criterion of instability is given for the imperfect Bose gas under the action of attraction.

DOI
10.7498/aps.55.1634

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Using the free energy and the equation of state for an imperfect Bose gas, the analytical expression between the critical temperature and the length of dispersion wave and the pressure for the imperfect Bose gas is derived. The unusual properties of the specific heat at constant pressure and the expansion coefficient at constant pressure and isothermal compressibility by the attractive force for the imperfect Bose gas are revealed. The instability arising from the attractive force is pointed out, and the temperature criterion and particle density criterion of instability is given for the imperfect Bose gas under the action of attraction.
Using the equation of free energy for a weakly interacting Fermi gas, the stability of a weakly interacting Fermi gas in the absence of external potential is studied by means of thermodynamics. The instability arising from the weakly attractive interacting of a Fermi gas is pointed out. The particle density criterion and the temperature criterion of instability for the imperfect Fermi gas with weakly attractive interaction are given, and the dependance of the critical density of particles on the temperature and the mass of particle and the attractive interaction is discussed.
The low-temperature properties of a weakly interacting Bose gas in weak magnetic field are studied by using the conclusion of a weakly interacting Bose gas in external potential.The expressions of total energy and heat capacity are given analytically.The effects of the interparticle interactions as well as magnetic field on the thermodynamic properties of the system are discussed.It is shown that repulsion(attraction) can make the spatial distribution of particle number and energy concentrate(disperse) and the chemical potential,total energy,heat capacity of system increase(decrease).While strengthen magnetic field,the spatial distribution of particle number and energy will tend to disperse and the effects of interaction on it will be weaken.The effects of interaction on the different eigenvalue exist different individual behaviors.
The ideal Bose gas has two major shortcomings: at zero temperature, all the particles 'condense' at zero energy or momentum, thus violating the Heisenberg principle; the second is that the pressure below the critical point is independent of density resulting in zero incompressibility (or infinite isothermal compressibility) which is unphysical. We propose a modification of the ideal Bose gas to take into account the Heisenberg principle. This modification results in a finite (in)compressibility at all temperatures and densities. The main properties of the ideal Bose gas are preserved, i.e. the relation between the critical temperature and density, but the specific heat has a maximum at the critical temperature instead of a discontinuity. Of course interactions are crucial for both cases in order to describe actual physical systems.
We show that the pressure of the Bogoliubov weakly imperfect Bose gas (WIBG) can be calculated exactly in the thermodynamic limit. We point out the sufficient and necessary conditions for it not to equate with the pressure of the ideal Bose gas (IBG). We prove that they differ only in that part of the phase diagram where the WIBG has a Bose condensate. We show that in contast to the conventional Bose condensate (e.g. in the IBG) the condensate in the WIBG is due to an effective attraction between bosons in the zero-mode.
Abstract This chapter describes the mechanism of Bose–Einstein condensation in the simplest ideal Bose gas case. An explicit expression for the critical temperature is derived in the analytically soluble case of a gas confined in a box. Various thermodynamic quantities are calculated above and below the critical temperature. Emphasis is given to the isothermal compressibility which diverges below the critical temperature. The behaviour of the off-diagonal one-body density matrix is discussed. Results for the fluctuations of the single-particle occupation numbers are derived in both the canonical and grand canonical ensembles.
We discuss the thermodynamics of a nonrelativistic gas of bosons with a local repulsive interaction. In particular, we compute the temperature and density dependences of pressure, energy and entropy densities, superfluid and condensate fractions, correlation length, specific heat, isothermal and adiabatic compressibilities, and various sound velocities. The $T\ensuremath{\rightarrow}0$ limit approaches the quantum phase transition, while the universal critical behavior of a classical second-order phase transition in the O(2) universality class determines the region around the critical temperature. Our nonperturbative flow equations based on exact functional renormalization cover all regions in the phase diagram.