Bose-Einstein Condensation in Some Interacting Systems
Sixty years after the discovery of Bose-Einstein condensation in the free Bose gas1, the following problem remains largely unsolved: is this phenomenon stable with respect to the introduction of a two-body interaction ? In this talk I shall present some results on two classes of interacting models, which though perhaps artificial may throw some light on the problem stated above. First I shall describe a one-dimensional gas of Bosons interacting through Neumann hard cores. Attractive boundary conditions or a weak gravitational potential are imposed on the system so that the corresponding non-interacting model exhibits Bose-Einstein condensation and singular thermodynamic functions.2,3 The second model we shall consider is the Van der Waal or Kac limit of a three-dimensional gas of Bosons interacting through a pair potential of positive type.4
KeywordsHard Core Pair Potential Einstein Condensation Free Energy Density Positive Type
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