Abstract
Thermodynamic quantities, occupation numbers and their fluctuations of a one-dimensional Bose gas confined by a harmonic potential are studied using different ensemble approaches. Combining number theory methods, a new approach is presented to calculate the occupation numbers of different energy levels in microcanonical ensemble. The visible difference of the ground state occupation number in grand-canonical ensemble and microcanonical ensemble is found to decrease by power law as the number of particles increases.
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