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THERMODYNAMIC PROPERTIES OF A q-BOSE GAS

Li Li

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

Basing on the Thomas-Fermi approximation or local density approximation(LDA) and the principle of the constancy of chemical potential in equilibrium,we calculate thermodynamic quantities of q-Bose gas,which include the critical temperature of BEC,the ground fraction of BEC,the total energy and the special heat of BEC.The criterion of BEc occurring and the criterion of the jump of special heat in BEC are derived.

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An analytical description of the low temperature behaviour of a trapped interacting Bose gas is presented by using a simple approach that is based on the principle of the constancy of chemical potentials in equilibrium and the local-density approximation. Several thermodynamic quantities, which include the ground-state fraction, chemical potential, total energy, entropy and heat capacity, are derived analytically. It is shown that the results obtained here are in excellent agreement with the experimental data and the theoretical predictions based on the numerical calculation. Meanwhile, by selecting a suitable variable, the divergent problem existing in some papers is solved.
The thermodynamical properties of interacting Bose atoms in a harmonic potential are studied within the mean-field approximation. For weak interactions, the quantum statistics is equivalent to an ideal gas in an effective mean-field potential. The eigenvalue of the Gross–Pitaevskii equation is identified as the chemical potential of the ideal gas. The condensation temperature and density profile of atoms are calculated. It is found that the critical temperature Tc decreases as the interactions increase. Below the critical point, the condensation fraction exhibits a universal relation of N0/N = 1-(T/Tc)γ, with the index γ ≈ 2.3 independent of the interaction strength, the chemical potential, as well as the frequency of the confining potential.
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