On the nature of Bose-Einstein condensation enhanced by localization

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

In a previous paper we established that for the perfect Bose gas and the mean-field Bose gas with an external random or weak potential, whenever there is generalized Bose-Einstein condensation in the eigenstates of the single particle Hamiltonian, there is also generalized condensation in the kinetic energy states. In these cases Bose-Einstein condensation is produced or enhanced by the external potential. In the present paper we establish a criterion for the absence of condensation in single kinetic energy states and prove that this criterion is satisfied for a class of random potentials and weak potentials. This means that the condensate is spread over an infinite number of states with low kinetic energy without any of them being macroscopically occupied.

Mots clés: Diagonal Particle Interactions; Generalized Bose-Einstein Condensation; Random Potentials; Integrated Density of States; Multiscale Analysis; Diagonal Particle Interactions.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]

Thomas Jaeck, Joseph V. Pulé, Valentin A. Zagrebnov. On the nature of Bose-Einstein condensation enhanced by localization. Journal of Mathematical Physics, 2010, 51 (10), pp.103302. ⟨10.1063/1.3488965⟩. ⟨hal-00493467v2⟩