Transition Temperature in One-Dimensional Bose-Einstein Condensation

摘要

The phase transition of the one-dimensional Bose gas, interacting weakly with a repulsive potential and trapped in an external parabolic potential, is studied in a mean field approximation. The Bose-Einstein condensed (BEC) state is identified by the non-vanishing thermal average of a bose field. Free energies between the BEC state and normal state are compared. A crossing of the free energies occurring at low temperature suggests the first order phase transition in an interacting one-dimensional bose system. From fitting of numerical results, the relation among the transition temperature T_c, the total number of bosons N and the interaction V is also provided as a simple power law, T_c ∝ (N~2V)~(2/3).