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arXiv:2511.13681

Damping of phonons in one-dimensional quantum fluids

Federica Cataldini, Nataliia Bazhan, Sabino, João, Philipp Schüttelkopf, Mohammadamin Tajik, Frederik Møller, Si-Cong Ji, Sebastian Erne, I. E. Mazets, Jörg Schmiedmayer

Published Nov 17, 2025• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2511.13681

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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 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.
In the hydrodynamics of integrable models, diffusion is a subleading correction to ballistic propagation. Here we quantify the diffusive contribution for one-dimensional Bose gases and find it most influential in the crossover between the main thermodynamic regimes of the gas. Analysing the experimentally measured dynamics of a single density mode, we find diffusion to be relevant only for high wavelength excitations. Instead, the observed relaxation is solely caused by a ballistically driven dephasing process, whose time scale is related to the phonon lifetime of the system and is thus useful to evaluate the applicability of the phonon bases typically used in quantum field simulators.
While the mechanisms governing the equilibrium properties of quantum gases are today relatively well understood, their non-equilibrium counterparts remain largely unknown. In this thesis, we theoretically explore the non-equilibrium physics of low-dimensional, interacting Bose gases in two representative configurations. In the first one, we consider an isolated Bose superfluid in two dimensions following a quench of the coupling constant. Using a quantum hydrodynamic description combined with a Keldysh field formalism, we derive quantum kinetic equations for the low-energy phononic excitations of the system. This enables us to describe the system's evolution from its short-time (prethermal) coherent dynamics to its long-time thermalization. In particular, we derive and discuss the Landau-Beliaev damping rates both in the standard perturbative approach and within a self-consistent extension of the theory. The results are also discussed in the light of recent experiments. Our second study explores a one-dimensional, periodically-driven quantum system, a Bose gas subjected to periodically-kicked interactions. In the limit of infinitely short kicks, this system was previously shown to exhibit a fast exponential spreading of the wave function. By revisiting this problem for kicks of arbitrary duration, we demonstrate that, in this case, the spreading is not exponential but sub-diffusive at long time. Our findings indicate that the breakdown of exponential spreading occurs at very short times even for extremely short kicks, suggesting that sub-diffusion is more the rule than the exception in that system.
At low temperatures, elementary excitations of a one-dimensional quantum liquid form a gas that can move as a whole with respect to the center of mass of the system. This internal motion attenuates at exponentially long time scales. As a result, in a broad range of frequencies, the liquid is described by two-fluid hydrodynamics, and the system supports two sound modes. The physical nature of the two sounds depends on whether the particles forming the quantum liquid have a spin degree of freedom. For particles with spin, the modes are analogous to the first and second sound modes in superfluid 4He^{4}\mathrm{He}4He, which are the waves of density and entropy, respectively. When dissipative processes are taken into account, we find that at low frequencies, the second sound is transformed into heat diffusion, while the first sound mode remains weakly damped and becomes the ordinary sound. In a spinless liquid, the entropy and density oscillations are strongly coupled and the resulting sound modes are hybrids of the first and second sound. As the frequency is lowered and dissipation processes become important, the crossover to a single-fluid regime occurs in two steps. First the hybrid modes transform into predominantly density and entropy waves, similar to the first and second sound, and then the density wave transforms to the ordinary sound and the entropy wave becomes a heat-diffusion mode. Finally, we account for the dissipation due to viscosity and intrinsic thermal conductivity of the gas of excitations, which controls attenuation of the sound modes at high frequencies.
Ultracold bosonic and fermionic quantum gases confined to quasi-one-dimensional (1D) geometry are promising candidates for probing fundamental concepts of Luttinger liquid (LL) physics. They can also be exploited for devising applications in quantum information processing and precision measurements. Here, we focus on 1D dipolar Bose gases, where evidence of super-strong coupling behavior has been demonstrated by analyzing the low-energy static and dynamical structures of the fluid at zero temperature by a combined reptation quantum Monte Carlo (RQMC) and bosonization approach. Fingerprints of LL behavior emerge in the whole crossover from the already strongly interacting Tonks–Girardeau at low density to a dipolar density wave regime at high density. We have also shown that a LL framework can be effectively set up and utilized to describe this strongly correlated crossover physics in the case of confined 1D geometries after using the results for the homogeneous system in LL hydrodynamic equations within a local density approximation. This leads to the prediction of observable quantities such as the frequencies of the collective modes of the trapped dipolar gas under the more realistic conditions that could be found in ongoing experiments. The present paper provides a description of the theoretical framework in which the above results have been worked out, making available all the detailed derivations of the hydrodynamic Luttinger equations for the inhomogeneous trapped gas and of the correlation functions for the homogeneous system.