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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2023
- DOI:
- 10.48550/arXiv.2311.05361
- arXiv:
- arXiv:2311.05361
- Bibcode:
- 2023arXiv231105361H
- Keywords:
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- Mathematical Physics;
- Mathematics - Spectral Theory;
- Quantum Physics;
- Primary 81V73;
- Secondary 81Q10;
- 47A10
- E-Print:
- 10 pages