One-dimensional Bose gases are a useful testing ground for quantum dynamics in many-body theory. They allow experimental tests of many-body theory predictions in an exponentially complex quantum system. Here we calculate the dynamics of a higher-order soliton in the mesoscopic case of $N={10}^{3}$ -- ${10}^{4}$ particles, giving predictions for quantum soliton breather relaxation. These quantum predictions use a truncated Wigner approximation, which is a $1/N$ expansion, in a regime where other exactly known predictions are recovered to high accuracy. Such dynamical calculations are testable in forthcoming Bose-Einstein-condensate experiments.One-dimensional Bose gases are a useful testing ground for quantum dynamics in many-body theory. They allow experimental tests of many-body theory predictions in an exponentially complex quantum system. Here we calculate the dynamics of a higher-order soliton in the mesoscopic case of $N={10}^{3}$--${10}^{4}$ particles, giving predictions for quantum soliton breather relaxation. These quantum predictions use a truncated Wigner approximation, which is a $1/N$ expansion, in a regime where other exactly known predictions are recovered to high accuracy. Such dynamical calculations are testable in forthcoming Bose-Einstein-condensate experiments.

arXiv:1708.01013Physical Review ANov 27, 201718 citations

Phonon scattering from spatial relaxation of one-dimensional Bose gases

Bilal Alilou, Clément Duval, Frederick Del Pozo +1 more

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

N={10}^{3}

{10}^{4}

particles, giving predictions for quantum soliton breather relaxation. These quantum predictions use a truncated Wigner approximation, which is a

1/N

expansion, in a regime where other exactly known predictions are recovered to high accuracy. Such dynamical calculations are testable in forthcoming Bose-Einstein-condensate experiments.

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.