Bose-Einstein condensation in a one-dimensional interacting system due to power-law trapping potentials

Abstract

We examine the possibility of Bose-Einstein condensation in one-dimensional interacting Bose gas subjected to confining potentials of the form $V_{\rm ext}(x)=V_0(|x|/a)^γ$, in which $γ< 2$, by solving the Gross-Pitaevskii equation within the semi-classical two-fluid model. The condensate fraction, chemical potential, ground state energy, and specific heat of the system are calculated for various values of interaction strengths. Our results show that a significant fraction of the particles is in the lowest energy state for finite number of particles at low temperature indicating a phase transition for weakly interacting systems.