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Physica B Condensed Matter

Thermodynamic properties and effective mass of a weakly-interacting Bose gas using the static fluctuation approximation

Mohamed K. Al-Sugheir, Diala E. Esbaih, B.R. Joudeh, H. B. Ghassib

Published May 8, 2023• 1 citation
Publisher
DOI
10.1016/j.physb.2023.414943

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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. 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 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.

arXiv:1010.3691•International Journal of Modern Physics B•Sep 30, 2010•8 citations
The static fluctuation approximation (SFA) is applied to compute the thermodynamic properties of a trapped two-dimensional (2D) interacting hard-sphere (HS) Bose gas in the weakly and strongly interacting regime. A mean-field approach involving a variational wave function is used to compute the mean-field energy as a function of temperature for each harmonic oscillator (HO) state plugged into the SFA technique. In the variational approach, a parameter $\ensuremath{\alpha}$ is introduced into the harmonic oscillator wave function in order to take into account the changes in the width when the repulsive interactions between the bosons are increased. In the weakly interacting regime, below the critical temperature, the total energy of all HO states (evaluated by our model) matches the noninteracting result very well. However, beyond the critical temperature, we ``fit'' our energies to the classical limit for 2D bosons in a trap by using a suitably proposed weighting function. We compare our results to earlier results of mean-field theory. Further, we evaluate the density matrix arising from correlations between the HO orbitals.
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. 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 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.