Damping of phase fluctuations in superfluid Bose gases

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.

6 pages, 4 figures, published version

References in corpus (5)

• Dynamic response of one-dimensional interacting fermions
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas
• Infrared behavior and spectral function of a Bose superfluid at zero temperature
• Unified picture of superfluidity: From Bogoliubov's approximation to Popov's hydrodynamic theory
• Quantum Heisenberg antiferromagnets in a uniform magnetic field: nonanalytic magnetic field dependence of the magnon spectrum