Thermodynamics of Finite Bose Systems: An Exact Canonical-Ensemble Treatment with Different Traps

摘要

Based on an exact canonical partition function, we investigate the thermodynamics and trap-size scaling behaviors for a finite number of ideal bosons confined in a cubic box or in a harmonic trap. Both in the box trap imposed by either periodic or Dirichlet boundary conditions (BCs) and in the harmonic trap, we calculate several physical quantities including the chemical potential mu, specific heat C_(N), condensate fraction /N, root-mean-square fluctuations (delta)n_(0) of the condensate population, and transition temperature T_(c), and compare these quantities under different traps. We discuss the particle-number dependence of T_(c) through proposing several T_(c) definitions, where the differences among these values are considerable for the finite systems.