Thermodynamics of a repulsive and attractive harmonically-trapped one-dimensional atomic Bose gas

A system of a finite number of harmonically-trapped bosons in one-dimension interacting through a contact repulsive or attractive potential is investigated. The static fluctuation approximation is used to calculate the chemical potential, condensate fraction, energy per particle, and heat capacity of the system. It is observed that an attractive potential increases the transition temperature and is therefore favorable for Bose–Einstein condensation. A peak appears in the heat capacity as the system becomes more attractive. The interaction type as well as its strength affects the calculated quantities below the transition temperature. For a weak interaction, the behavior of thermodynamic properties is close to that of non-interacting trapped bosons.