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Do bosons condense in a homogeneous magnetic field? (English) Zbl 1097.82002
Summary: It has been known since the paper of M. R. Schafroth [Phys. Rev. 100, 463–475 (1955)] and then due to a rigorous result of N. Angelescu and A. Corciovei [Rev. Roum. Phys. 20, 661–671 (1975)] that the answer to the question in the title is negative for a three-dimensional “ideal gas of charged bosons”. The present paper adds a new rigorous result in this direction. We show that the answer to the question becomes positive, if this “ideal gas of charged bosons” is simultaneously embedded in an appropriate periodic external potential. We prove that it is true for the Perfect Bose Gas (PBG), as well as for the Imperfect Bose Gas with a Mean-Field repulsive particle interaction.

82B10 Quantum equilibrium statistical mechanics (general)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
82D05 Statistical mechanics of gases
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