Fortschritte der Physik

Discrete Bose‐Einstein systems in a box with low adiabatic invariant

Valentin I. Vlad, N. I. Ionescu-Pallas

Published Apr 24, 2003• 3 citations

Abstract

Abstract The Bose‐Einstein energy spectrum of an ideal quantum gas confined in a box is discrete and strongly dependent on the box geometry and temperature, for low product of the atomic mass number, Aat and the adiabatic invariant, TV2/3, i.e. on γ = Aat TV2/3. Even within the approximation of non‐interacting particles in the gas, the calculation of the thermodynamic properties of Bose‐Einstein systems turns out to be a difficult mathematical problem. The present study compares the total number of particles, the total energy and the specific heat obtained by sums over the discrete states to the results of the approximate integrals (for defined values of γ) and shows the noticeable errors of the last ones at low adiabatic invariant (around condensation). Then, more rigorous and precise analytical approximations of sums are found in the case of finite number of atoms (correlated with the existence of a zero energy level) and the finite volume of the gas. The corrected thermodynamic functions depend on γ (for fixed fugacity). The condensation temperature is corrected also in order to describe more accurately the discrete Bose‐Einstein systems. Under these circumstances, the analysis of the specific heat leads to the conclusion that it shows no discontinuity, for the entire range of γ values.

DOI: 10.1002/prop.200310069

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