Abstract
We study the perfect Bose gas in random external potentials and show that there is generalized Bose-Einstein condensation in the random eigenstates if and only if the same occurs in the one-particle kinetic-energy eigenstates, which corresponds to the generalized condensation of the free Bose gas. Moreover, we prove that the amounts of both condensate densities are equal. Our method is based on the derivation of an explicit formula for the occupation measure in the one-body kinetic-energy eigenstates which describes the repartition of particles among these non-random states. This technique can be adapted to re-examine the properties of the perfect Bose gas in the presence of weak (scaled) non-random potentials, for which we establish similar results. In addition some of our results can be applied to models with diagonal interactions, that is, models which conserve the occupation density in each single particle eigenstate.
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T. Jaeck is PhD student at UCD and Université de la Méditerranée (Aix-Marseille II, France).
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Jaeck, T., Pulé, J.V. & Zagrebnov, V.A. On the Nature of Bose-Einstein Condensation in Disordered Systems. J Stat Phys 137, 19–55 (2009). https://doi.org/10.1007/s10955-009-9825-y
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DOI: https://doi.org/10.1007/s10955-009-9825-y