Damping of phase fluctuations in superfluid Bose gases

Original · EN

Using Popov's hydrodynamic approach we derive an effective Euclidean action for the long-wavelength phase fluctuations of superfluid Bose gases in D dimensions. We then use this action to calculate the damping of phase fluctuations at zero temperature as a function of D. For D >1 and wavevectors | k | << 2 mc (where m is the mass of the bosons and c is the sound velocity) we find that the damping in units of the phonon energy Eₖ = c | k | is to leading order gammaₖ / Eₖ = AD (k₀ᵈ / 2 pi rho) (| k | / k₀)² ᵈ ⁻², where rho is the boson density and k₀ =2 mc is the inverse healing length. For D -> 1 the numerical coefficient AD vanishes and the damping is proportional to an additional power of |k | /k₀; a self-consistent calculation yields in this case gammaₖ / Eₖ = 1.32 (k₀ / 2 pi rho)¹/² |k | / k₀. In one dimension, we also calculate the entire spectral function of phase fluctuations.