Phonon scattering from spatial relaxation of one-dimensional Bose gases

Bilal Alilou; Clément Duval; Frederick Del Pozo; Nicolas Cherroret

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arXiv · 2511.14861

Phonon scattering from spatial relaxation of one-dimensional Bose gases

Bilal Alilou·Clément Duval·Frederick Del Pozo·Nicolas Cherroret

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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 $\smash{\gamma_k\propto k^{3/2}}$ 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.

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Bilal Alilou, Clément Duval, Frederick Del Pozo, Nicolas Cherroret. 2025-11-18. Phonon scattering from spatial relaxation of one-dimensional Bose gases. https://arxiv.org/abs/2511.14861

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