Thermodynamic properties of an interacting hard-sphere Bose gas in a trap using the static fluctuation approximation

TL;DR

This paper investigates the thermodynamic properties of a weakly-interacting hard-sphere Bose gas in a trap at finite temperatures using the static fluctuation approximation, revealing how particle number and interactions influence system behavior.

Contribution

It introduces a detailed analysis of thermodynamic properties of a trapped hard-sphere Bose gas using the static fluctuation approximation, highlighting the impact of particle number and interaction strength.

Findings

Particle number significantly influences thermodynamic properties.

Critical temperature decreases with increased repulsion.

Energy fluctuations are much smaller than the energy itself.

Abstract

A hard-sphere (HS) Bose gas in a trap is investigated at finite temperatures in the weakly-interacting regime and its thermodynamic properties are evaluated using the static fluctuation approximation (SFA). The energies are calculated with a second-quantized many-body Hamiltonian and a harmonic oscillator wave function. The specific heat capacity, internal energy, pressure, entropy and the Bose-Einstein (BE) occupation number of the system are determined as functions of temperature and for various values of interaction strength and number of particles. It is found that the number of particles plays a more profound role in the determination of the thermodynamic properties of the system than the HS diameter characterizing the interaction, that the critical temperature drops with the increase of the repulsion between the bosons, and that the fluctuations in the energy are much smaller than the energy itself in the weakly-interacting regime.