Phonon scattering from spatial relaxation of one-dimensional Bose gases

Abstract

We theoretically investigate the nonequilibrium relaxation of a spatial density modulation in a one-dimensional, weakly interacting Bose gas, and its connection to the equilibrium scattering rate ${\gamma }_k\propto k^{3/2}$ of the system's phononic excitations. We show that the relaxation is generally governed by a nonequilibrium scattering rate ${\gamma }_{k,t}$ coupled to quantum fluctuations, which approaches its equilibrium value ${\gamma }_k$ only at long times. Numerical simulations of quantum kinetic equations reveal an algebraic convergence, ${\gamma }_{k,t}-{\gamma }_k\sim t^{-2/3}$, confirmed by analytical predictions. More broadly, our results establish a theoretical framework for experimentally probing phonon dynamics through the temporal evolution of local perturbations in quantum gases.