Complete Bose–Einstein condensation in the Gross–Pitaevskii regime

Boccato, Chiara; Brennecke, Christian; Cenatiempo, Serena; Schlein, Benjamin (2018). Complete Bose–Einstein condensation in the Gross–Pitaevskii regime. Communications in Mathematical Physics, 359(3):975-1026.

Abstract

We consider a gas of N bosons in a box with volume one interacting through a two-body potential with scattering length of order (Formula presented.) (Gross–Pitaevskii limit). Assuming the (unscaled) potential to be sufficiently weak, we prove complete Bose–Einstein condensation for the ground state and for many-body states with finite excitation energy in the limit of large N with a uniform (N-independent) bound on the number of excitations.

Abstract

We consider a gas of N bosons in a box with volume one interacting through a two-body potential with scattering length of order (Formula presented.) (Gross–Pitaevskii limit). Assuming the (unscaled) potential to be sufficiently weak, we prove complete Bose–Einstein condensation for the ground state and for many-body states with finite excitation energy in the limit of large N with a uniform (N-independent) bound on the number of excitations.

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