TY - JOUR A1 - Idziaszek, Zbigniew A1 - Gajda, M. A1 - Navez, Patrick A1 - Wilkens, Martin A1 - Rzazewski, Kazimierz T1 - Fluctuation of the Weakly Interacting Bose-Einstein Condensate N2 - 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. Y1 - 1999 ER - TY - JOUR A1 - Idziaszek, Zbigniew A1 - Wilkens, Martin T1 - Scattering of atoms on the Bose-Einstein condensate N2 - We investigate the scattering of slowly moving atoms on the Bose-Einstein condensate. The condensate excitations are described by Bogolyubov-de Gennes equatins. We derive the analytic expressions for the differential cross section for both elastic and ineladtic channels. For the elastic channel we obtain analytic results for total cross sections, and discuss their scaling with the number of condensed atoms. For inelastic channels we present numerical results for the total cross section. Y1 - 1999 ER -