On the nature of Bose-Einstein condensation in disordered systems

Thomas Jaeck (1) , Joseph V. Pulé (1) , Valentin A. Zagrebnov (2, 3)

1 Department of Mathematical Physics
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

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.

Mots clés: Generalized Bose-Einstein Condensation; Random Potentials; Integrated Density of States; Lifshitz Tails

Domaines: Physique mathématique [math-ph]

Thomas Jaeck, Joseph V. Pulé, Valentin A. Zagrebnov. On the nature of Bose-Einstein condensation in disordered systems. Journal of Statistical Physics, 2009, 137 (1), pp.19-55. ⟨10.1007/s10955-009-9825-y⟩. ⟨hal-00389565⟩