Influence of boundary conditions on the growth of condensate fraction in a finite Bose system

Abstract

In a recent paper we carried out a rigorous, asymptotic analysis of the low-temperature behavior of a Bose gas confined to a finite cubic geometry and subjected to periodic boundary conditions. That analysis is now extended to Dirichlet, Neumann, and antiperiodic boundary conditions. As before, the thermogeometric parameter $y$ and the condensate fraction $\frac{{N}_{0}}{N}$ are studied as functions of temperature and are evaluated explicity for cubes with $\frac{L}{\overline{l}}=40 \mathrm{and} 100$, where $L$ is the edge length of the enclosure and $\overline{l}$ the mean interparticle distance in the system. The finite-size corrections to the condensate fraction under Dirichlet or Neumann boundary conditions turn out to be qualitatively different from those under periodic or antiperiodic boundary conditions. This difference becomes manifest when one tries to express these corrections in a form consistent with the standard scaling theory for finite-size effects.