A note on spontaneous symmetry breaking in the mean-field Bose gas
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908468910227456 |
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| author | Deuchert, Andreas Nam, Phan Thanh Napiorkowski, Marcin |
| author_facet | Deuchert, Andreas Nam, Phan Thanh Napiorkowski, Marcin |
| contents | We consider the homogeneous Bose gas in the three-dimensional unit torus, where $N$ particles interact via a two-body potential of the form $N^{-1} v(x)$. The system is studied at inverse temperatures of order $N^{-2/3}$, which corresponds to the temperature scale of the Bose--Einstein condensation phase transition. We show that spontaneous $U(1)$ symmetry breaking occurs if and only if the system exhibits Bose--Einstein condensation in the sense that the one-particle density matrix of the Gibbs state has a macroscopic eigenvalue. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_19402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on spontaneous symmetry breaking in the mean-field Bose gas Deuchert, Andreas Nam, Phan Thanh Napiorkowski, Marcin Mathematical Physics Analysis of PDEs Quantum Physics We consider the homogeneous Bose gas in the three-dimensional unit torus, where $N$ particles interact via a two-body potential of the form $N^{-1} v(x)$. The system is studied at inverse temperatures of order $N^{-2/3}$, which corresponds to the temperature scale of the Bose--Einstein condensation phase transition. We show that spontaneous $U(1)$ symmetry breaking occurs if and only if the system exhibits Bose--Einstein condensation in the sense that the one-particle density matrix of the Gibbs state has a macroscopic eigenvalue. |
| title | A note on spontaneous symmetry breaking in the mean-field Bose gas |
| topic | Mathematical Physics Analysis of PDEs Quantum Physics |
| url | https://arxiv.org/abs/2501.19402 |