Linear Response in the s.c. Bogolyubov model of Bose-Einstein Condensation

We discuss the linear response of the Bogolyubov theory of a weakly interacting Bose gas below the critical temperature. The specific aspects, due to induced perturbation terms in the self-consistent treatment are discussed in detail. We show that Bogolyubov's model having a gap-less equilibrium spectrum nevertheless gives rise to an effective susceptibility which does not satisfy the super-fluidity criterion of Hohenberg and Martin.

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