Eur. Phys. J. B (2012) 85: 370
https://doi.org/10.1140/epjb/e2012-30639-3

Regular Article

Damping of phase fluctuations in superfluid Bose gases

¹ Institut für Theoretische Physik, Universität Frankfurt, Max-von-Laue Strasse 1, 60438 Frankfurt, Germany
² Department of Physics, University of Florida, 32611 Gainesville, FL, USA

^a e-mail: lange@itp.uni-frankfurt.de

Received: 18 July 2012
Received in final form: 12 September 2012
Published online: 14 November 2012

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| ≪ 2mc (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 γ_k/E_k = A_D(k₀^D/2πρ)(|k|/k₀)^2D-2, where ρ is the boson density and k₀ = 2mc 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|/k₀; a self-consistent calculation yields in this case γ_k/E_k = 1.32 (k₀/2πρ)^1/2|k|/k₀. In one dimension, we also calculate the entire spectral function of phase fluctuations.