Hartre-Fock calculation for trapped, two-dimensional interacting Bose gases of finite size

Abstract

The mean-field properties of trapped, two-dimensional interacting Bose gases of finite size are surveyed numerically. The coupled nonlinear equations of the Gross-Pitaevskii (GP) equation and the Hartree-Fock equation for the condensate and the thermal component, respectively, are calculated by the hybrid method, in which the GP equation and the low-lying excitations less than cut-off energy are calculated quantum mechanically using the basis representation, while the high-lying states are obtained within the local density approximation. Consistent solutions are obtained for the whole range of temperatures including the critical temperature by determining the thermodynamic chemical potential mu from the condition that the total atomic number must be the desired value, instead of identifying mu with the eigenvalue of the GP equation. Comparisons with the results of the semiclassical two-fluid model are presented.