Title: Bose condensation in (random) traps
Author(s):

	Th. Jaeck (School of Mathematical Sciences, University College Dublin Belfield, Dublin 4, Ireland) ,
	J.V. Pulé (School of Mathematical Sciences, University College Dublin Belfield, Dublin 4, Ireland) ,
	V.A. Zagrebnov (Université de la Méditerranée (Aix-Marseille II), Centre de Physique Théorique - UMR 6207 CNRS, Luminy - Case 907, 13288 Marseille, Cedex 09, France)

We study a non-interacting (perfect) Bose-gas in random external potentials (traps). It is shown that a generalized Bose-Einstein condensation in the random eigenstates manifests 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. This statement is relevant for justification of the Bogoliubov approximation} in the theory of disordered boson systems.

Key words: generalized Bose-Einstein condensation, random potentials, integrated density of states, Lifshitz tails
PACS: 05.30.Jp, 03.75.Fi, 67.40.-w

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