Mullin, WJ2024-04-262024-04-262000-01-01https://hdl.handle.net/20.500.14394/41010Published version located at http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVH-41B6CCX-4&_user=1516330&_coverDate=07%2F31%2F2000&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1513271713&_rerunOrigin=google&_acct=C000053443&_version=1&_urlVersion=0&_userid=1516330&md5=2353a1a26cd8ba94192c68a55fcba4f5&searchtype=aWe 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.Bose-Einstein condensationideal Bose gaspermutation cyclesPhysicsarticle