Exponential bounds of the condensation for dilute Bose gases
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- by Phan Thành Nam and Simone Rademacher;
- Trans. Amer. Math. Soc. 378 (2025), 3229-3278
- DOI: https://doi.org/10.1090/tran/9335
- Published electronically: March 5, 2025
- HTML | PDF
Abstract:
We consider $N$ bosons on the unit torus $\Lambda =[0,1]^3$ in the Gross-Pitaevski regime where the interaction potential scales as $N^2 v(N(x-y))$. We prove that the low-lying eigenfunctions and the Gibbs state at low temperatures exhibit the Bose-Einstein condensation in a strong sense, namely the probability of having $n$ particles outside of the condensation decays exponentially in $n$.References
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Bibliographic Information
- Phan Thành Nam
- Affiliation: Department of Mathematics, LMU Munich, Theresienstrasse 39, 80333 Munich, Germany
- MR Author ID: 850145
- ORCID: 0000-0001-7599-9742
- Email: nam@math.lmu.de
- Simone Rademacher
- Affiliation: Department of Mathematics, LMU Munich, Theresienstrasse 39, 80333 Munich, Germany
- MR Author ID: 1159031
- ORCID: 0000-0001-5059-4466
- Email: simone.rademacher@math.lmu.de
- Received by editor(s): December 13, 2023
- Received by editor(s) in revised form: August 14, 2024
- Published electronically: March 5, 2025
- Additional Notes: This work was partially funded by the Deutsche Forschungsgemeinschaft (DFG project Nr. 426365943).
- © Copyright 2025 by the authors
- Journal: Trans. Amer. Math. Soc. 378 (2025), 3229-3278
- MSC (2020): Primary 81V70, 82B10
- DOI: https://doi.org/10.1090/tran/9335