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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

cond-mat.quant-gasquant-phSubmitted Nov 18, 2025• Announced Nov 20, 2025• 0 citations
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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 $\smash{γ_k\propto k^{3/2}}$ 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.

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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 γk∝k3/2\smash{γ_k\propto k^{3/2}}γk​∝k3/2 of the system's phononic excitations. We show that the relaxation is generally governed by a nonequilibrium scattering rate γk,tγ_{k,t}γk,t​ coupled to quantum fluctuations, which approaches its equilibrium value γkγ_kγk​ only at long times. Numerical simulations of quantum kinetic equations reveal an algebraic convergence, γk,t−γk∼t−2/3\smash{γ_{k,t} - γ_k \sim t^{-2/3}}γk,t​−γk​∼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.
Collective excitations in one-dimensional (1D) quantum fluids are expected to propagate almost without dissipation. Here we directly excite phonon modes in a weakly interacting 1D Bose gas and study their time evolution. In the linear response regime, damping is surprisingly fast and quantitatively follows the non-analytic scaling predicted by Andreev's hydrodynamic description. For stronger excitations, we observe a crossover to a highly nonlinear regime characterized by wave breaking, captured by the finite-temperature nonlinear Schrödinger evolution. Our results resolve a long-standing question on the fate of phonons in 1D Bose gases, and open new pathways to study non-linear relaxation in quantum many-body systems.
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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 T2ph{T}_{2}\mathrm{ph}T2​ph. T2ph{T}_{2}\mathrm{ph}T2​ph scales inversely with the system size and is much smaller than currently experimentally accessible.
This thesis manuscript is devoted to different aspects of the non-equilibrium dynamics of a moving two-dimensional ultra-cold Bose gas, under the simultaneous action of a spatially disordered potential and interactions between particles. In the absence of interactions, the momentum distribution of the gas is the sum of two well-known components: a classical, diffusive background made of particles multiply scattered by the disorder, and a coherent backscattering interference peak (CBS peak), consequence of the weak localization phenomenon. In the presence of weak interactions, mean field simulations show that these two contributions evolve in time. This evolution is described by two coupled kinetic equations, which we derive using a microscopic quantum transport theory. These predict the destruction of the CBS peak by an effective dephasing mechanism, and the thermalization of the diffusive background. As the interaction strength increases, the effects of disorder become negligible, and the dynamics of the gas resembles that of a superfluid. In this regime, the gas quickly enters a so-called "pre-thermal" state: the spatial correlations g_1 decrease algebraically and propagate along a light cone, in accordance with theoretical predictions. Finally, at long times, our simulations describe the global evolution of the system towards a thermal equilibrium state, characterized by a Kosterlitz-Thouless transition separating a normal fluid state from a superfluid state. Some properties of this phase transition, resulting from the non-equilibrium evolution in the presence of disorder, are discussed.
We present a theoretical analysis of spatial correlations in a one-dimensional driven-dissipative nonequilibrium condensate. Starting from a stochastic generalized Gross-Pitaevskii equation, we derive a noisy Kuramoto-Sivashinsky equation for the phase dynamics. For sufficiently strong interactions, the coherence decays exponentially in close analogy to the equilibrium Bose gas. When interactions are small on a scale set by the nonequilibrium condition, we find through numerical simulations a crossover between a Gaussian and exponential decay with peculiar scaling of the coherence length on the fluid density and noise strength.
This work investigates the theoretical and experimental decoherence of phonons in weakly and strongly-interacting Bose-Einstein Condensates (BECs). The theoretical analysis treats phonons as open quantum systems where the environment comprises all other quasi-particle modes of the BEC. The phonons are assumed to be Gaussian states and the time in which they decohere is estimated from the evolution of their purity and nonclassical depth in the dissipative channel. The calculations are performed for various BEC systems and it is found that the excited phonon states will always decohere much more rapidly than the rate at which they relax back to equilibrium with the environment. Part II of this work considers how the decoherence of the phonons can be measured experimentally. The experiment that is currently being investigated uses a strongly-interacting [superscript]6Li BEC where the scattering length can be varied with an external magnetic field. In a strongly-interacting Bose gas the mutual interaction between the condensed and noncondensed components plays a greater role than in weakly-interacting gases and results in distinct absorption images. Understanding the effects from this mutual interaction is vital to model the in-situ absorption images of a strongly-interacting BEC in order to extract accurate information such as that which will facilitate the experimental measurement of decoherence. Three theoretical models that could be used to fit in-situ absorption images of a strongly-interacting gas are analysed. These are the bi-modal, semi-ideal and Hartree-Fock models, which will be fit against the absorption images of the [superscript]6Li BEC for various scattering lengths. The validity of these models is also investigated to determine when beyond mean-field effects may be observed in the Bose gas. Controlling decoherence is essential to the operation and physical realisation of many quantum information tasks and quantum technologies. Recently, new technologies have emerged from relativistic quantum information science that, in principle, are more precise than their non-relativistic counterparts. The practical setup of these devices utilizes phonons of BECs but the decoherence of the phonons has not been considered. In this work, one of the BEC systems used to estimate the decoherence time of the phonons has been chosen to be based on these devices. This calculation is expected to inform the practical realization of these devices and inspire future related studies. Analogue gravity investigations based on BECs also utilize phonons, for example, in the analogue of Hawking radiation. The quantum properties of these states is of particular interest in these studies and understanding how they decohere, and at what rate, could potentially inform the theory of black hole physics as well as dictate what is possible to measure experimentally.