Long Cycles in a Perturbed Mean Field Model of a Boson Gas

Dorlas, T. C. and Martin, Philippe A. and Pulé, J. V. (2005) Long Cycles in a Perturbed Mean Field Model of a Boson Gas. Journal of Statistical Physics, 121 (3-4). pp. 433-461. ISSN 0022-4715

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Official URL: http://doi.org/10.1007/s10955-005-7582-0


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 = ρ_short + ρ_long into the number density of particles belonging to cycles of finite length (ρ_short) and to infinitely long cycles (ρ_long) in the thermodynamic limit. For this model we prove that when there is Bose condensation, ρ_long 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 ρ_long =/= 0 with off-diagonal long range order and winding paths that occur in the path integral representation of the Bose gas.

Item Type: Article
Uncontrolled Keywords: Bose-Einstein Condensation, Cycles, Large Deviations, Perturbed Mean Field Model
Divisions: School of Theoretical Physics > Preprints
Date Deposited: 05 Oct 2017 19:31
Last Modified: 15 Dec 2022 15:11
URI: https://dair.dias.ie/id/eprint/165

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