A Lower Bound on the Critical Momentum of an Impurity in a Bose-Einstein Condensate

Abstract

In the Bogoliubov-Fröhlich model, we prove that an impurity immersed in a Bose-Einstein condensate forms a stable quasi-particle when the total momentum is less than its mass times the speed of sound. The system thus exhibits superfluid behavior, as this quasi-particle does not experience friction. We do not assume any infrared or ultraviolet regularization of the model, which contains massless excitations and point-like interactions.

10 pages, version accepted for publication in Comptes Rendus Mathématique

References in corpus (4)

• Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED
• On Existence of Ground States in the Spin Boson Model
• Hamiltonians for polaron models with subcritical ultraviolet singularities
• Non-Fock Ground States in the Translation-Invariant Nelson Model Revisited Non-Perturbatively

Cited by in corpus (1)

• The excitation spectrum of a Bose gas with an impurity in the Gross-Pitaevskii regime