1. Exactness of the Bogoliubov approximation in random external potentials
- Author
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Valentin A. Zagrebnov, Thomas Jaeck, Department of Mathematical Physics, University College Dublin [Dublin] (UCD), Centre de Physique Théorique - UMR 6207 (CPT), Centre National de la Recherche Scientifique (CNRS)-Université de Toulon (UTLN)-Université de Provence - Aix-Marseille 1-Université de la Méditerranée - Aix-Marseille 2, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), and Université de la Méditerranée - Aix-Marseille 2-Université de Provence - Aix-Marseille 1-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Bogoliubov c-number Approximation ,Infinitesimal ,[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph] ,FOS: Physical sciences ,Kinetic energy ,01 natural sciences ,law.invention ,Momentum ,Generalized Bose-Einstein Condensation ,law ,Variational principle ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,0103 physical sciences ,010306 general physics ,Mathematical Physics ,Mathematical physics ,Physics ,Condensed Matter::Quantum Gases ,Stochastic process ,Berezin-Lieb Inequalities ,Condensed Matter::Other ,Condensation ,05.30.Jp, 03.75.Fi, 67.40.-w ,Statistical and Nonlinear Physics ,Mathematical Physics (math-ph) ,Thermodynamic limit ,010307 mathematical physics ,Bose–Einstein condensate ,Bogoliubov Quasi-Averages ,Random Potentials - Abstract
International audience; We investigate the validity of the Bogoliubov c-number approximation in the case of interacting Bose-gas in a \textit{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.
- Published
- 2010