Crossover of Quasiparticles and Statistics of Bose-Einstein Condensate with Increasing Interaction: from an Ideal Gas to a Thomas-Fermi Regime. The Case of a One-Dimensional Flat Trap
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A change-over of the quasiparticle wave functions and spectrum under a variation in an interparticle interaction in a Bose-Einstein condensed gas of bosons confined in a one-dimensional trap with a flat potential and impermeable walls is studied analytically and numerically. An efficient approximate method of analysis is developed. It yields a solution to the self-consistent Bogoliubov and Gross-Pitaevskii equations for quasiparticles and the condensate that describes a crossover from the regime of a gas of noninteracting bosons to the regime of a gas with the interaction being strong enough to reach a Thomas-Fermi asymptotics. As a result, the characteristic function of the total number of noncondensed particles is found which, for the first time, allows one to figure out how the quantum statistics of fluctuations of the number of particles in the condensate depends on its inhomogeneity and the interparticle interaction in the case of the flat trap. The qualitative features of this dependence as well as a possibility of an experimental observation of the predicted effects in the actual traps are discussed.
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