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arXiv:2603.02182

Universal Behavior on the Relaxation Dynamics of Far-From-Equilibrium Quantum Fluids

Sarah Sab, Michelle A. Moreno-Armijos, Arnol Daniel Garcia Orozco, Gabriel V. Fernandes, Ying Zhu, A. R. Fritsch, Hélène Perrin, Sergey Nazarenko, Vanderlei Salvador Bagnato

Published Mar 2, 2026• 0 citations
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Abstract

Investigating the initial conditions that lead many-body quantum systems to an out-of-equilibrium state is fundamental for understanding their thermalization dynamics. In this work we observe the relaxation for two regimes of excitation that can drive the turbulent Bose-Einstein condensate into two distinct final states, and are defined by the amount of energy injected into the system. The subcritical regime is characterized by a lower injection of energy, which can lead to an inverse particle cascade and, consequently, to the BEC mode repopulation during the relaxation process. The supercritical regime is marked by a higher energy injection, that may lead to the BEC dissolution and a final thermal state. In both cases we observe relaxation stages that exhibit the same key features: a direct cascade, a non-thermal fixed point with the same exponents, a prethermalization region and, finally, the thermalization of the system. In the final thermalization stage, universal scaling is observed for both regimes, even though their final states are completely different. By analyzing the coherence length of our turbulent cloud, we clearly visualize the recovery and the loss of the coherence for the subcritical and supercritical regimes after relaxation. These results indicate that the evolution of turbulence occurs independent of its initial conditions and of the final state achieved.

DOI
10.48550/arxiv.2603.02182

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Investigating the initial conditions that lead many-body quantum systems to an out-of-equilibrium state is fundamental for understanding their thermalization dynamics. In this work we observe the relaxation for two regimes of excitation that can drive the turbulent Bose-Einstein condensate into two distinct final states, and are defined by the amount of energy injected into the system. The subcritical regime is characterized by a lower injection of energy, which can lead to an inverse particle cascade and, consequently, to the BEC mode repopulation during the relaxation process. The supercritical regime is marked by a higher energy injection, that may lead to the BEC dissolution and a final thermal state. In both cases we observe relaxation stages that exhibit the same key features: a direct cascade, a non-thermal fixed point with the same exponents, a prethermalization region and, finally, the thermalization of the system. In the final thermalization stage, universal scaling is observed for both regimes, even though their final states are completely different. By analyzing the coherence length of our turbulent cloud, we clearly visualize the recovery and the loss of the coherence for the subcritical and supercritical regimes after relaxation. These results indicate that the evolution of turbulence occurs independent of its initial conditions and of the final state achieved.
The dynamics of nonequilibrium closed quantum systems and their route to thermalization are of fundamental interest to several fields, from cosmology to particle physics. However, a comprehensive description of nonequilibrium phenomena still presents a significant challenge. In this work, we report the observation of distinct stages during the relaxation of the decaying turbulence in trapped Bose-Einstein condensates. Our findings show a direct particle cascade from low to high momenta, a consequence of the energy injection in the system, exhibiting a characteristic universal scaling. This stage is followed by an inverse particle cascade responsible for repopulating the previously depleted condensate. Both cascades can be explained through self-similar solutions provided by wave turbulence theory. These findings provide important insights into the relaxation stages of out-of-equilibrium quantum many-body systems.
We investigate the emergence and evolution of turbulence in Bose-Einstein condensates driven far from equilibrium through a controlled energy injection. By applying a timeperiodic modulation for a fixed duration, we trigger nonequilibrium dynamics that lead to the formation of a turbulent state characterized by a complex distribution of excitations and density fluctuations. Our study focuses on the post-excitation relaxation process, where we observe a transient broadening of the momentum distribution: a signature of a direct energy cascade followed by an inverse particle cascade due to the nonlinear intra-scales energy transfer. Through systematic analysis based on the nonthermal fixed points and weak wave turbulence theories, we identify universal scaling laws governing the repopulation dynamics of the condensate. These findings advance our understanding of turbulent relaxation pathways in superfluids while enhancing the understanding of driven-dissipative quantum systems.
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Starting with a Bose-Einstein Condensate of Rb atoms in equilibrium, the System is brought to turbulence and left to relax under the occurrence of reactions from the introduced excitations. The typical phenomena of the evolution to establishment of the turbulence states are observed. After excitation is removed, the system begins to relax, giving way to diverse phenomena such as the presence of non-thermal fixed points, pre-thermalization and finally equilibrium with or without the reconstitution of the condensate depending of the quantity of injected energy. The work paves the way for the study of the thermalization of an out-of-equilibrium many-body quantum system.
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Using a non-perturbative quantum kinetic framework, we develop a unified description of the far-from-equilibrium dynamics of three-dimensional Bose gases following cooling quenches across the Bose-Einstein condensation transition. By tracking the spatio-temporal evolution of the momentum distribution, we show that the equilibrium condensation threshold simultaneously acts as a dynamical critical point, separating distinct far-from-equilibrium universality classes governed by different non-equilibrium attractors. While quenches above the transition exhibit a single-timescale relaxation toward a thermal fixed point, quenches below the transition display a crossover from a transient weak-turbulence regime to a coarsening fixed point governed by the diffusive recombination of vortex lines. Quenches directly to the condensation threshold, finally, are controlled by a previously unidentified critical fixed point characterized by the superdiffusive spreading of critical fluctuations and a distinct set of dynamical exponents. Together, these dynamical scaling laws establish a far-from-equilibrium counterpart of the condensation phase transition, in which the equilibrium critical point also organizes the long-time non-equilibrium dynamics.