Permutation cycles in the Bose-Einstein condensation of a trapped ideal gas
Journal or Book Title
We consider Bose–Einstein condensation for non-interacting particles trapped in a harmonic potential by considering the length of permutation cycles arising from wave function symmetry. This approach had been considered previously by Matsubara and Feynman for a homogeneous gas in a box with periodic boundary conditions. For the ideal gas in a harmonic potential, one can treat the problem nearly exactly by analytical means. One clearly sees that the noncondensate is made up of permutation loops that are of length less-than-or-equals, slantN1/3, and that the phase transition consists of the sudden growth of longer permutation cycles. The condensate is seen to consist of cycles of all possible lengths with nearly equal likelihood.
Mullin, WJ, "Permutation cycles in the Bose-Einstein condensation of a trapped ideal gas" (2000). Physics Department Faculty Publication Series. 47.