Thermodynamics of Bose–Einstein gas trapped in [formula omitted]-dimensional quartic potentials

Abstract

Quartic potentials play an important role in a broad range of fields in the Bose–Einstein Condensation (BEC) literature, from optical lattices to vortices and even to the quantum phase transitions. This also makes the study of thermodynamic properties of systems confined by these potentials interesting. For this purpose, the BEC of an ideal Bose system with a finite number of particles is considered in three and lower dimensions. A comprehensive thermodynamic analysis including the condensation temperature, chemical potential, condensate fraction, heat capacity, total energy, and entropy has been carried out with a special emphasis on low-dimensional case for which the standard semi-classical method is not applicable. As a result of our calculations based on a quantum mechanical treatment we have shown that BEC is possible in a one-dimensional quartic potential, in contrast with the predictions of the standard method. Moreover it is also possible to corroborate our results by using a modified semi-classical approximation that enables us to estimate the condensation temperatures for one-dimensional traps for all powers of the confining potential. We have found higher condensation temperatures than for the harmonic traps for all the three spatial configurations of the quartic trap.