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Complete Bose–Einstein Condensation in the Gross–Pitaevskii Regime

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 \({N^{-1}}\) (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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Correspondence to Benjamin Schlein.

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Communicated by R. Seiringer

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Boccato, C., Brennecke, C., Cenatiempo, S. et al. Complete Bose–Einstein Condensation in the Gross–Pitaevskii Regime. Commun. Math. Phys. 359, 975–1026 (2018). https://doi.org/10.1007/s00220-017-3016-5

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  • DOI: https://doi.org/10.1007/s00220-017-3016-5