@article{RzazewskiGoralCironeetal.2001, author = {Rzazewski, Kazimierz and Goral, K. and Cirone, M. A. and Wilkens, Martin}, title = {Bose-Einstein Condensation of two interacting particles}, year = {2001}, abstract = {We investigate the notion of Bose-Einstein condensation of interacting particles. The definition of the condensate is based on the existence of the dominant eigenvalue of the single-particle density matrix. The statistical properies and the characteristics temperature are computed exactly in the soluble models of two interacting atoms.}, language = {en} } @article{IdziaszekGajdaNavezetal.1999, author = {Idziaszek, Zbigniew and Gajda, M. and Navez, Patrick and Wilkens, Martin and Rzazewski, Kazimierz}, title = {Fluctuation of the Weakly Interacting Bose-Einstein Condensate}, year = {1999}, abstract = {We consider the role of weak interaction on the fluctuations of the number of condensed atoms within canonical and microanonical ensembles. Unlike the correspinding 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.}, language = {en} } @article{BuschEnglertRzazewskietal.1998, author = {Busch, Thomas and Englert, Bertold-Georg and Rzazewski, Kazimierz and Wilkens, Martin}, title = {Two cold atoms in a harmonic trap}, year = {1998}, abstract = {Two ultracold atoms moving in a trap interact weakly at a very short distance. This interaction can be modeled by a properly regularized contact potential. We solve the corresponding time-independent Schr{\"o}dinger equation under the assumption of a parabolic, spherically symmetric trapping potential.}, language = {en} }