We theoretically investigate the nonequilibrium relaxation of a spatial density modulation in a one-dimensional nonintegrable 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 density relaxation is generically governed by a nonequilibrium scattering rate ${\gamma }_{k,t}$ coupled to the time dependence of phonon occupations, 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.

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• Bose gases
• Low-dimensional models
• Phonons
• Quantum kinetic theory
• Nonequilibrium Green's function