In the Bogoliubov theory a condensate initially prepared in its ground statedescribed by stationary Bogoliubov vacuum and later perturbed by atime-dependent potential or interaction strength evolves into a time-dependentexcited state which is dynamical Bogoliubov vacuum. The dynamical vacuum has asimple diagonal form in a time-dependent orthonormal basis of single particlemodes. This diagonal representation leads to a gaussian probabilitydistribution for possible outcomes of density measurements in position andmomentum space. In these notes we also discuss relations with the U(1) symmetrybreaking version of the Bogoliubov theory and give two equivalent gaussianintegral representations of the dynamical vacuum state.
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