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arXiv:2408.11109 · Physical review. B./Physical review. B

Statistical prethermalization in a randomly kicked many-body classical rotor system

Aritra Kundu, Tanay Nag, Atanu Rajak

Published Jun 23, 2025• 2 citations
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Abstract

We explore the phenomena of prethermalization in a many-body classical system of rotors under aperiodic drives characterised by waiting time distribution (WTD), where the waiting time is defined as the time between two consecutive kicks. We consider here two types of aperiodic drives: random and quasi-periodic. We observe a short-lived pseudo-thermal regime with algebraic suppression of heating for the random drive where WTD has an infinite tail, as observed for Poisson and binomial kick sequences. On the other hand, quasi-periodic drive characterised by a WTD with a sharp cut-off, observed for Thue-Morse sequence of kick, leads to prethermal region where heating is exponentially suppressed. The kinetic energy growth is analyzed using an average surprise associated with WTD quantifying the randomness of drive. In all of the aperiodic drives we obtain the chaotic heating regime for late time, however, the diffusion constant gets renormalized by the average surprise of WTD in comparison to the periodic case.

DOI
10.1103/lhnv-1l4l

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We explore the phenomena of prethermalization in a many-body classical system of rotors under aperiodic drives characterised by waiting time distribution (WTD), where the waiting time is defined as the time between two consecutive kicks. We consider here two types of aperiodic drives: random and quasi-periodic. We observe a short-lived pseudo-thermal regime with algebraic suppression of heating for the random drive where WTD has an infinite tail, as observed for Poisson and binomial kick sequences. On the other hand, quasi-periodic drive characterised by a WTD with a sharp cut-off, observed for Thue-Morse sequence of kick, leads to prethermal region where heating is exponentially suppressed. The kinetic energy growth is analyzed using an average surprise associated with WTD quantifying the randomness of drive. In all of the aperiodic drives we obtain the chaotic heating regime for late time, however, the diffusion constant gets renormalized by the average surprise of WTD in comparison to the periodic case.
Driven many-body systems typically experience heating due to the lack of energy conservation. Heating may be suppressed for time-periodic drives, but little is known for less regular drive protocols. In this paper, we investigate the heating dynamics in aperiodically kicked systems, specifically those driven by quasiperiodic Thue-Morse or a family of sequences with n -multipolar temporal correlations. We demonstrate that multiple heating channels can be eliminated . The number of eliminated channels increases with multipolar order n . We illustrate this in a classical kicked rotor chain where we find a long-lived prethermal regime. When the static Hamiltonian only involves the kinetic energy, the prethermal lifetime t* can strongly depend on the temporal correlations of the drive, with a power-law dependence on the t*∼K−2n , for which we can account using a simple linearization argument. Published by the American Physical Society 2024
A many-body interacting system of classical kicked rotor serves as a prototypical model for studying Floquet heating dynamics. Having established the fact that this system exhibits a long-lived prethermal phase with a quasiconserved average Hamiltonian before entering into the chaotic heating regime, we use spatiotemporal fluctuation correlation of kinetic energy as a two-point observable to probe the above dynamic phases. We remarkably find the diffusive transport of fluctuation in the prethermal regime suggesting an underlying hydrodynamic picture in a generalized Gibbs ensemble with a definite temperature that depends on the driving parameter and the initial conditions. On the other hand, the heating regime is characterized by a diffusive growth of kinetic energy where the correlation is sharply localized around the fluctuation center for all time. Consequently, we attribute nondiffusive and nonlocalized structure of correlation to the crossover regime, connecting the prethermal phase to the heating phase, where the kinetic energy displays a complicated growth structure. We understand these numerical findings using the notion of relative phase matching where the prethermal phase (heating regime) refers to an effectively coupled (isolated) nature of the rotors. We exploit the statistical uncorrelated nature of the angles of the rotors in the heating regime to find the analytical form of the correlator that mimics our numerical results in a convincing way.
We introduce well-defined characterizations of prethermal states in realistic periodically driven many-body systems with unbounded chaotic diffusion of the kinetic energy. These systems, interacting arrays of periodically kicked rotors, are paradigmatic models of many-body chaos theory. We show that the prethermal states in these systems are well described by a generalized Gibbs ensemble based essentially on the average Hamiltonian. The latter is the quasiconserved quantity in the prethermal state and the ensemble is characterized by the temperature of the state. An explicit exact expression for this temperature is derived. Using also arguments based on chaos theory, we demonstrate that the lifetime of the prethermal state is exponentially long in the inverse of the temperature, in units of the driving frequency squared. Our analytical results, in particular those for the temperature and the lifetime of the prethermal state, agree well with numerical observations.
Periodically driven classical many-body systems can host a rich zoo of prethermal dynamical phases. In this work, we extend the paradigm of classical prethermalization to aperiodically driven systems. We establish the existence of a long-lived prethermal regime in spin systems subjected to random multipolar drives. We demonstrate that the thermalization time scales as (1/T)^{2n+2}, where n is the multipolar order and T is the intrinsic time-scale associated with the drive. In the n→∞ limit, the drive becomes quasiperiodic and the thermalization time becomes exponentially long [∼exp(β/T)]. We further establish the robustness of prethermalization by demonstrating that these thermalization time scaling laws hold for a wide range of initial state energy densities. Intriguingly, the thermalization process in these classical systems is parametrically slower than their quantum counterparts, thereby highlighting important differences between classical and quantum prethermalization. Finally, we propose a protocol to harness this classical prethermalization to realize time rondeau crystals.
Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the timescale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with n-multipolar correlations, corresponding to a polynomially suppressed low-frequency spectrum. For n≥1, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent 2n+1. A simple theory based on Fermi's golden rule accounts for this behavior. The quasiperiodic Thue-Morse sequence corresponds to the n→∞ limit and, accordingly, exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile nonequilibrium phases, which we illustrate with a random multipolar discrete time crystal.
The nonequilibrium quantum dynamics of closed many-body systems is a rich yet challenging field. While recent progress for periodically driven (Floquet) systems has yielded a number of rigorous results, our understanding on quantum many-body systems driven by rapidly varying but aperiodic and quasiperiodic driving is still limited. Here, we derive rigorous, nonperturbative, bounds on the heating rate in quantum many-body systems under Thue-Morse quasiperiodic driving and under random multipolar driving, the latter being a tunably randomized variant of the former. In the process, we derive a static effective Hamiltonian that describes the transient prethermal state, including the dynamics of local observables. Our bound for Thue-Morse quasiperiodic driving suggests that the heating time scales like (ω/g)^{-C ln(ω/g)} with a positive constant C and a typical energy scale g of the Hamiltonian, in agreement with our numerical simulations.