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Momentum distribution functions in ensembles: the inequivalence of microcannonical and canonical ensembles in a finite ultracold system



Momentum distribution functions in ensembles: the inequivalence of microcannonical and canonical ensembles in a finite ultracold system



Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics 88(2): 022113



It is demonstrated in many thermodynamic textbooks that the equivalence of the different ensembles is achieved in the thermodynamic limit. In this present work we discuss the inequivalence of microcanonical and canonical ensembles in a finite ultracold system at low energies. We calculate the microcanonical momentum distribution function (MDF) in a system of identical fermions (bosons). We find that the microcanonical MDF deviates from the canonical one, which is the Fermi-Dirac (Bose-Einstein) function, in a finite system at low energies where the single-particle density of states and its inverse are finite.

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Accession: 054452628

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PMID: 24032781

DOI: 10.1103/PhysRevE.88.022113


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