arXiv:1010.0425 · Journal of Mathematical Physics

Exactness of the Bogoliubov approximation in random external potentials

Thomas Jaeck, Valentin Anatol'evich Zagrebnov

Published Dec 1, 2010• 2 citations

Abstract

We investigate the validity of the Bogoliubov c-number approximation in the case of interacting Bose-gas in a homogeneous random media. To take into account the possible occurence of type III generalized Bose–Einstein condensation (i.e., the occurrence of condensation in an infinitesimal band of low kinetic energy modes without macroscopic occupation of any of them) we generalize the c-number substitution procedure to this band of modes with low momentum. We show that, as in the case of the one-mode condensation for translation-invariant interacting systems, this procedure has no effect on the exact value of the pressure in the thermodynamic limit, assuming that the c-numbers are chosen according to a suitable variational principle. We then discuss the relation between these c-numbers and the (total) density of the condensate.

DOI: 10.1063/1.3521495

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