Quantum oscillators model to derive an ideal gas in Bose-Einstein condensates under gravitation of earth

Abstract

Considering a set of condensates as N indistinguishable noninteracting quantum oscillators and replacing an available volume with a harmonic volume, we derived an ideal gas model by applying the canonical partition function via the thermodynamic relation. In this case, we take a longitudinal part of the three-dimensional Gross-Pitaevskii equation in which the effect of gravitation of earth works. Since we used the time-independent perturbation theory, to include gravity effect, we must put the higher coefficient in the formulation of each energy state whose value is determined by the separated amplitude formula in each state. It will also be shown that even though the equation of state represents an ideal gas, the appropriate heat capacity approaches Einstein’s solid-like model if the certain conditions are employed.