Damping of phase fluctuations in superfluid Bose gases

TL;DR

This paper derives an effective theory for phase fluctuations in superfluid Bose gases and calculates their damping at zero temperature across different dimensions, revealing how damping behavior varies with dimensionality.

Contribution

It introduces a hydrodynamic approach to derive an effective action and computes the damping of phase fluctuations, including a self-consistent calculation in one dimension.

Findings

Damping scales with wavevector as a power law depending on dimension.

In 1D, damping is proportional to an additional power of wavevector.

Spectral function of phase fluctuations is fully calculated in 1D.

Abstract

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 E_k = c | k | is to leading order gamma_k / E_k = A_D (k_0^D / 2 pi rho) (| k | / k_0)^{2 D -2}, where rho is the boson density and k_0 =2 mc is the inverse healing length. For D -> 1 the numerical coefficient A_D vanishes and the damping is proportional to an additional power of |k | /k_0; a self-consistent calculation yields in this case gamma_k / E_k = 1.32 (k_0 / 2 pi rho)^{1/2} |k | / k_0. In one dimension, we also calculate the entire spectral function of phase fluctuations.