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Entropy

Emergent Particle Cascade in a Periodically Driven One-Dimensional Interacting Bose–Hubbard System

Zhenmeng Zhang, J Liu, Yongqiang Li

Published Oct 27, 2026• 0 citations
Publisher

Abstract

Cascade is known as the transfer of conserved quantities across scales through nonlinear mode coupling. Originally studied in classical fluids, it has recently been realized in quantum systems. However, whether a stable cascade can emerge in a strongly interacting quantum system during the driving process remains an open question, where heating competes with the cascade. In this work, we investigate the far-from-equilibrium dynamics of a one-dimensional Bose–Hubbard system at half-filling, driven periodically by a spatially modulated chemical potential that injects energy at a single intermediate wavevector. By performing large-scale simulations, we uncover that the momentum distribution follows a quasi-steady power-law scaling in the region [π/4,π/2]. Notably, this particle cascade in momentum space is stable only under weak driving in the weakly interacting regime against thermalization, while it persists up to substantially larger amplitudes in the strongly interacting regime. Our results reveal an interacting many-body quantum counterpart of periodically driven turbulent wave cascades and indicate a mechanism by which interactions stabilize universal distributions under far-from-equilibrium conditions.

DOI
10.3390/e28111183

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Cascade is known as the transfer of conserved quantities across scales through nonlinear mode coupling. Originally studied in classical fluids, it has recently been realized in quantum systems. However, whether a stable cascade can emerge in a strongly interacting quantum system during the driving process remains an open question, where heating competes with the cascade. In this work, we investigate the far-from-equilibrium dynamics of a one-dimensional Bose–Hubbard system at half-filling, driven periodically by a spatially modulated chemical potential that injects energy at a single intermediate wavevector. By performing large-scale simulations, we uncover that the momentum distribution follows a quasi-steady power-law scaling in the region [π/4,π/2]. Notably, this particle cascade in momentum space is stable only under weak driving in the weakly interacting regime against thermalization, while it persists up to substantially larger amplitudes in the strongly interacting regime. Our results reveal an interacting many-body quantum counterpart of periodically driven turbulent wave cascades and indicate a mechanism by which interactions stabilize universal distributions under far-from-equilibrium conditions.
We study the out-of-equilibrium dynamics of a weakly interacting one-dimensional Bose gas in a box trap, subjected to a drive realized by a periodically oscillating linear potential. After a transient regime, the gas reaches a quasi-steady state, characterized by the presence of several solitons. At weak driving amplitude, the solitons are only weakly perturbed by one another, while at strong driving amplitude a regime analogous to turbulence is reached, where the solitons are strongly intertwined with each other. We show that a hallmark of both regimes can be found in the momentum distribution, which displays a power-law decay n(k)∼k−2n(k) \sim k^{-2}n(k)∼k−2 at weak driving amplitude and n(k)∼k−αn(k) \sim k^{-α}n(k)∼k−α with a power-law exponent α∈[7,9]α\in [7,9]α∈[7,9] at large amplitude. We further characterize each of the two regimes by following the space-time maps and characterizing the solitons using the inverse scattering transform. The protocol analyzed in this study is amenable to experimental realization in current experimental setups.
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We explore prethermal Floquet steady states and instabilities of the weakly interacting two-dimensional Bose-Hubbard model subject to periodic driving. We develop a description of the nonequilibrium dynamics, at arbitrary drive strength and frequency, using a weak-coupling conserving approximation. We establish the regimes in which conventional (zero-momentum) and unconventional [(π,π)-momentum] condensates are stable on intermediate time scales. We find that condensate stability is enhanced by increasing the drive strength, because this decreases the bandwidth of quasiparticle excitations and thus impedes resonant absorption and heating. Our results are directly relevant to a number of current experiments with ultracold bosons.
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.
Nonequilibrium equations of state can provide an effective thermodynamic-like description of far-from-equilibrium systems. We experimentally construct such an equation for a direct energy cascade in a turbulent two-dimensional Bose gas. Our homogeneous gas is continuously driven on a large length scale and, with matching dissipation on a small length scale, exhibits a nonthermal but stationary power-law momentum distribution. Our equation of state links the cascade amplitude with the underlying scale-invariant energy flux, and can, for different drive strengths, gas densities, and interaction strengths, be recast into a universal power-law form using scalings consistent with the Gross-Pitaevskii model.
Abstract Understanding the relaxation dynamics of isolated quantum systems remains a central challenge in nonequilibrium physics. In this short review, we discuss recent experimental and theoretical advances in universal dynamics of turbulent Bose gases, with particular emphasis on nonthermal fixed points and wave turbulence in our experimental system at the São Carlos Institute of Physics of the University of São Paulo. We highlight the emergence of self-similar scaling behavior and its connection to particle and energy transport across momentum scales. In addition, we discuss an approach in which a differential equation has a universal scaling solution, providing a practical framework for extracting universal exponents from limited regions of the momentum distribution. Furthermore, we recap experimental observations of direct and inverse cascades in a three–dimensional trapped Bose–Einstein condensate, revealing distinct relaxation stages governed by universal scaling laws. These results demonstrate that turbulence plays a key role in far–from–equilibrium dynamics, offering a unified perspective on transport processes and thermalization in quantum many–body systems.