Second Sound in a Low-Temperature Weakly Interacting Bose Gas

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Abstract
Second sound in a weakly interacting Bose gas at low temperatures is described from a purely microscopic viewpoint. The simplicity of the model, which is specified by a single scattering length, allows a precise field theoretic analysis within the framework of equilibrium statistical mechanics in the weak coupling limit. The dispersion formula ν = c2q − iτq2 + O(q3) for the frequency of the second sound ν in terms of its wavenumber q is established. The leading terms in the low‐temperature limit of the constants c2 and τ are evaluated exactly.