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Long Cycles in a Perturbed Mean Field Model of a Boson Gas |
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| Authors: | Teunis C. Dorlas Philippe A. Martin Joseph V. Pule |
| Affiliation: | (1) School of Theoretical Physics, Dublin Institute for Advanced Studies, 10, Burlington Road, Dublin 4, Ireland;(2) Institut of Theoretical Physics, Swiss Federal Institute for Technology (EPFL), CH 1015 Lausanne, Switzerland;(3) UCD School of Mathematical Sciences, University College Dublin, Dublin 4, Belfield, Ireland |
| Abstract: | In this paper we give a precise mathematical formulation of the relation between Bose condensation and long cycles and prove its validity for the perturbed mean field model of a Bose gas. We decompose the total density ρ=ρshort+ρlong into the number density of particles belonging to cycles of finite length (ρshort) and to infinitely long cycles (ρlong) in the thermodynamic limit. For this model we prove that when there is Bose condensation, ρlong is different from zero and identical to the condensate density. This is achieved through an application of the theory of large deviations. We discuss the possible equivalence of ρlong≠ 0 with off-diagonal long range order and winding paths that occur in the path integral representation of the Bose gas |
| Keywords: | Bose– Einstein condensation cycles large deviations perturbed mean field model |
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