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 $\smash{ \gamma_k\propto k^{ 3/2}}$ 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, $\smash{ \gamma_{ k,t} - \gamma_k \sim t^{ -2/3}}$, 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.
Categories: cond-mat.quant-gas quant-ph