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Permutation Cycles In The Bose-Einstein Condensation Of A Trapped Ideal Gas, Wj Mullin
Permutation Cycles In The Bose-Einstein Condensation Of A Trapped Ideal Gas, Wj Mullin
William J. Mullin
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 …
The Condensate Number In Pimc Treatments Of Trapped Bosons, Wj Mullin, Sd Heinrichs, Jp Fernandez
The Condensate Number In Pimc Treatments Of Trapped Bosons, Wj Mullin, Sd Heinrichs, Jp Fernandez
William J. Mullin
In path integral Monte Carlo (PIMC) treatments of harmonically trapped bosons, one cannot use the usual long-range constant limit of the one-body reduced density matrix ρ1 to determine the condensate number n0 because ρ1 always approaches zero in a trap. W. Krauth found that the longest permutation cycle arising in the simulation gives a consistent value of n0. Our analytical studies of the ideal gas suggest other ways of using permutation cycles to determine n0. We test these approaches on simulations involving finite-size ideal and interacting gases and find that the methods are consistent.