A note on spontaneous symmetry breaking in the mean-field Bose gas

• URL: http://arxiv.org/abs/2501.19402v3
• Date: Mon, 28 Jul 2025 12:06:14 GMT
• Title: A note on spontaneous symmetry breaking in the mean-field Bose gas
• Authors: Andreas Deuchert, Phan Thanh Nam, Marcin Napiorkowski,
• Abstract summary: We consider the homogeneous Bose gas in the three-dimensional unit torus, where $N$ particles interact via a two-body potential of the form $N-1 v(x)$.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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