Phys. Rev. Lett. 82, 4376 (1999)
Zbigniew Idziaszek, Mariusz Gajda, Patrick Navez, Martin Wilkens, and Kazimierz Rzążewski
We consider the role of weak interatomic interactions on the fluctuations of the number of condensed atoms within canonical and microcanonical ensembles. Unlike the corresponding case of the ideal gas this is not a clean, well-defined problem of mathematical physics. Two related reasons are the following: there is no unique way of defining the condensate fraction of the interacting system and no exact energy levels of the interacting system are known.
Sep 14, 1999
Soluble model of many interacting quantum particles in a trap
Magdalena A. Załuska-Kotur, Mariusz Gajda, Arkadiusz Orłowski, and Jan Mostowski
Exact solutions to many-body interacting systems of both bosonic and fermionic particles confined to harmonic potential in an arbitrary number of dimensions are given. Energy levels and their degeneracies for trapped identical particles interacting via harmonic forces are calculated. This specific form of the interaction allows for analytical solutions. The mutual interaction, attractive or repulsive, modifies significantly the properties of the considered system. For a large number of particles the interaction essentially results in a frequency shift. Statistical properties (e.g., microcanonical and grand canonical partition functions) as well as some illustrative, physically relevant examples are discussed. Our results give an unusual opportunity for further studies of interacting systems in the framework of the exactly soluble model.
Phys. Rev. A 61, 033613 (2000)
Exact solutions to many-body interacting systems of both bosonic and fermionic particles confined to harmonic potential in an arbitrary number of dimensions are given. Energy levels and their degeneracies for trapped identical particles interacting via harmonic forces are calculated. This specific form of the interaction allows for analytical solutions. The mutual interaction, attractive or repulsive, modifies significantly the properties of the considered system. For a large number of particles the interaction essentially results in a frequency shift. Statistical properties (e.g., microcanonical and grand canonical partition functions) as well as some illustrative, physically relevant examples are discussed. Our results give an unusual opportunity for further studies of interacting systems in the framework of the exactly soluble model.
Phys. Rev. A 61, 033613 (2000)
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