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A note on spontaneous symmetry breaking in the mean-field Bose gas
Andreas Deuchert1, Phan Thành Nam2, Marcin Napiórkowski3
1Department of Mathematics, Virginia Tech, 225 Stanger Street, Blacksburg, VA 24060-1026 USA.
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 . The system is studied at inverse temperatures of order , 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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