Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 116, Issue 5-6, Pages 1545-1578Publisher
SPRINGER
DOI: 10.1023/B:JOSS.0000041748.02351.07
Keywords
Bose-Einstein Condensation; magnetic field; Landau levels; periodic external potential; Perfect/Imperfect Bose Gas
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It has been known since the paper((26)) and then due to a rigorous result((3)) 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.
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