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

TL;DR

This paper analyzes the linear response of the Bogolyubov model for a weakly interacting Bose gas below the critical temperature, revealing discrepancies with superfluidity criteria despite a gapless spectrum.

Contribution

It provides a detailed discussion of the induced perturbation effects in the self-consistent Bogolyubov theory and highlights its limitations regarding superfluidity.

Findings

Bogolyubov model has a gapless spectrum

Effective susceptibility does not satisfy superfluidity criterion

Induced perturbation terms are crucial in the response analysis

Abstract

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.