Abstract
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 μ, specific heat C N , condensate fraction 〈n 0〉/N, root-mean-square fluctuations δ 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.
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