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We study a model describing a rotating linear rigid molicule interacting with a Bose-Einstein condensate. A generalization of the Landau criterion is established and gives the limit for which the molecule moves translationally and rotationally into the condensate without any friction. In particular, we show that the rotational energy released by the molecule is large enough to eject one atom out of the condensate. The detection of such an atom provides a direct measurement of the low-energy cross section of the scattering with the rotating molecule. Finally, increases of inertia and of centrifugal distortion of the molecule due to the surrounding condensate are estimated and compared with the experimental data obtained for a He4 droplet.
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.
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.
We derive exact thermodynamic identities relating the average number of condensed atoms and the root-mean- square fluctuations determined in different statistical ensembles for the weakly interacting Bose gas confined in a box. This is achieved by introducing the concept of auxiliary partition functions for model Hamiltonians that do conserve the total number of particles. Exploiting such thermodynamic identities, we provide the first, completely analytical prediction of the microcanonical particle number fluctuations in the weakly interacting Bose gas. Such fluctuations, as a function of the volume V of the box are found to behave normally, in contrast wiht the anomalous scaling behaviour V3/ 4 of the fluctuations in the ideal Bose gas.
We investigate the quantization of nonzero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy which always gives reward if played against any classical strategy.