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 $\smash{γ_k\propto k^{3/2}}$ of the system's phononic excitations. We show that the relaxation is generally governed by a nonequilibrium scattering rate $γ_{k,t}$ coupled to quantum fluctuations, which approaches its equilibrium value $γ_k$ only at long times. Numerical simulations of quantum kinetic equations reveal an algebraic convergence, $\smash{γ_{k,t} - γ_k \sim t^{-2/3}}$ , 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.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 $\smash{γ_k\propto k^{3/2}}$ of the system's phononic excitations. We show that the relaxation is generally governed by a nonequilibrium scattering rate $γ_{k,t}$ coupled to quantum fluctuations, which approaches its equilibrium value $γ_k$ only at long times. Numerical simulations of quantum kinetic equations reveal an algebraic convergence, $\smash{γ_{k,t} - γ_k \sim t^{-2/3}}$, 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.

cond-mat.quant-gasCross-listedarXiv:2511.14861Nov 20, 20250 citations

Phonon excitations in a one dimensional Bose gas

Federica Cataldini, Bernhard Rauer, Thomas Schweigler +4 more

Bulletin of the American Physical SocietyMar 5, 20190 citations

Role of thermal two-phonon scattering for impurity dynamics in a low-dimensional Bose-Einstein condensate

Tobias Lausch, Artur Widera, Michael Fleischhauer

We numerically study the relaxation dynamics of a single, heavy impurity atom interacting with a finite one- or two-dimensional, ultracold Bose gas. While there is a clear separation of time scales between processes resulting from single- and two-phonon scattering in three spatial dimensions, the thermalization in lower dimensions is dominated by two-phonon processes. This is due to infrared divergences in the corresponding scattering rates in the thermodynamic limit, which are a manifestation of the Mermin-Wagner-Hohenberg theorem. This makes it necessary to include second-order phonon scattering above a crossover temperature ${T}_{2}\mathrm{ph}$ . ${T}_{2}\mathrm{ph}$ scales inversely with the system size and is much smaller than currently experimentally accessible.We numerically study the relaxation dynamics of a single, heavy impurity atom interacting with a finite one- or two-dimensional, ultracold Bose gas. While there is a clear separation of time scales between processes resulting from single- and two-phonon scattering in three spatial dimensions, the thermalization in lower dimensions is dominated by two-phonon processes. This is due to infrared divergences in the corresponding scattering rates in the thermodynamic limit, which are a manifestation of the Mermin-Wagner-Hohenberg theorem. This makes it necessary to include second-order phonon scattering above a crossover temperature ${T}_{2}\mathrm{ph}$. ${T}_{2}\mathrm{ph}$ scales inversely with the system size and is much smaller than currently experimentally accessible.

arXiv:1712.07912Physical Review AMar 26, 201815 citations

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{γ_k\propto k^{3/2}}

of the system's phononic excitations. We show that the relaxation is generally governed by a nonequilibrium scattering rate

γ_{k,t}

coupled to quantum fluctuations, which approaches its equilibrium value

γ_k

only at long times. Numerical simulations of quantum kinetic equations reveal an algebraic convergence,

\smash{γ_{k,t} - γ_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.

{T}_{2}\mathrm{ph}

{T}_{2}\mathrm{ph}

scales inversely with the system size and is much smaller than currently experimentally accessible.