No Bose-Einstein Condensation in Closed Systems with Linear Dynamics

Recently Bose-Einstein condensation has gathered a popularity and interest. An interesting theoretical phenomenon closely related to BEC and condensation is Frohlich's dynamic condensation phenomenon, proposed as a reoccurring mechanism in biophysics. This phenomenon studied classically brings forth a hypothesis that dynamic emergence of condensation requires nonlinear interactions. Working in the purely quantum regime I show the correctness of the hypothesis for a broad class of initial states as well as show a way for condensation to emerge from linear dynamics if the initial state has very large or very long-range quantum correlations.