Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. E

Reservoir-induced stabilization of a periodically driven classical spin chain: Local versus global relaxation

Thomas Veness, Kay Brandner

Published Oct 27, 2023• 4 citations
Publisher

Abstract

Floquet theory is an indispensable tool for analyzing periodically driven quantum many-body systems. Although it does not universally extend to classical systems, some of its methodologies can be adopted in the presence of well-separated timescales. Here we use these tools to investigate the stroboscopic behaviors of a classical spin chain that is driven by a periodic magnetic field and coupled to a thermal reservoir. We detail and expand our previous work: we investigate the significance of higher-order corrections to the classical Floquet-Magnus expansion in both the high- and low-frequency regimes; explicitly probe the evolution dynamics of the reservoir; and further explore how the driven system and the reservoir synchronize with the applied field at low frequencies. In line with our earlier results, we find that the high-frequency regime is characterized by a local Floquet-Gibbs ensemble with the reservoir acting as a nearly-reversible heat sink. At low frequencies, the driven system rapidly enters a synchronized state, which can only be fully described in a global picture accounting for the concurrent relaxation of the reservoir in a fictitious magnetic field arising from the drive. We highlight how the evolving nature of the reservoir may still be incorporated in a local picture by introducing an effective temperature. Finally, we show that generic local-dissipation models that account for the influence of the reservoir on the driven system phenomenologically through Markovian dissipative equations of motion can generally not reproduce the rich behavior that our microscopic simulations reveal. In particular, such models prove insufficient to account for the suppression of overall energy absorption that is induced by the here observed synchronization between driven system and reservoir.

DOI
10.1103/physreve.108.044147

Related papers

Reservoir-induced stabilisation of a periodically driven classical spin chain: local vs. global relaxation

Thomas Veness, Kay Brandner

Floquet theory is an indispensable tool for analysing periodically-driven quantum many-body systems. Although it does not universally extend to classical systems, some of its methodologies can be adopted in the presence of well-separated timescales. Here we use these tools to investigate the stroboscopic behaviours of a classical spin chain that is driven by a periodic magnetic field and coupled to a thermal reservoir. We detail and expand our previous work: we investigate the significance of higher-order corrections to the classical Floquet-Magnus expansion in both the high- and low-frequency regimes; explicitly probe the evolution the dynamics of the reservoir; and further explore how the driven system synchronises with the applied field at low frequencies. In line with our earlier results, we find that the high-frequency regime is characterised by a local Floquet-Gibbs ensemble with the reservoir acting as a nearly-reversible heatsink. At low frequencies, the driven system rapidly enters a synchronised state, which can only be fully described in a global picture accounting for the concurrent relaxation of the reservoir in a fictitious magnetic field arising from the drive. We highlight how the evolving nature of the reservoir may still be incorporated in a local picture by introducing an effective temperature. Finally, we argue that dissipative equations of motion for periodically-driven many-body systems, at least at intermediate frequencies, must generically be non-Markovian.

arXiv:2208.08998•Aug 18, 2022•0 citations

Reservoir-induced stabilization of a periodically driven many-body system

Thomas Veness, Kay Brandner

Exploiting the rich phenomenology of periodically driven many-body systems is notoriously hindered by persistent heating in both the classical and the quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir makes stabilization of a nontrivial steady state possible. To this end, we model both the system and the reservoir as classical spin chains where driving is applied through a rotating magnetic field, and we simulate the Hamiltonian dynamics of this setup. We find that the intuitive limits of infinite frequency and vanishing frequency, where the system dynamics is governed by the average and the instantaneous Hamiltonian, respectively, can be smoothly extended into entire regimes separated only by a small crossover region. At high frequencies, the driven system stroboscopically attains a Floquet-type Gibbs state at the reservoir temperature. At low frequencies, a global synchronized Gibbs state emerges, whose temperature may depart significantly from the initial temperature of the reservoir. Although our analysis in some parts relies on the specific properties of our setup, we argue that much of its phenomenology could be generic.

Physical review. E•Oct 27, 2023•3 citations

Reservoir-induced stabilisation of a periodically driven many-body system

Thomas Veness, Kay Brandner

Exploiting the rich phenomenology of periodically-driven many-body systems is notoriously hindered by persistent heating in both the classical and quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir makes stabilisation of a non-trivial steady state possible. To this end, we model both the system and the reservoir as classical spin chains where driving is applied through a rotating magnetic field, and simulate the Hamiltonian dynamics of this setup. We find that the intuitive limits of infinite and vanishing frequency, where the system dynamics is governed by the average and the instantaneous Hamiltonian, respectively, can be smoothly extended into entire regimes separated only by a small crossover region. At high frequencies, the driven system stroboscopically attains a Floquet-type Gibbs state at the reservoir temperature. At low frequencies, a synchronised Gibbs state emerges, whose temperature may depart significantly from that of the reservoir. Although our analysis in some parts relies on the specific properties our setup, we argue that much of its phenomenology should be generic for a large class of systems.

arXiv:2208.08996•Aug 18, 2022•0 citations

Floquet prethermalization in periodically driven classical spin systems

Takashi Mori

It is proved that the energy absorption in a periodically driven classical spin system is exponentially slow in frequency, which results in a two-step relaxation called the Floquet prethermalization. This result is shown by establishing the classical limit of the quantum spin dynamics. The Floquet prethermal state is well described by the Gibbs ensemble with respect to the static effective Hamiltonian obtained by a truncation of the Floquet-Magnus expansion. On the other hand, the same effective Hamiltonian does not reproduce the local dynamics for an exponentially long time. This is due to the chaoticity of classical dynamics and in stark contrast to quantum spin systems, in which the effective Hamiltonian well reproduces the exact quantum dynamics up to an exponentially long time.

arXiv:1804.02165•Physical review. B./Physical review. B•Sep 10, 2018•61 citations

Benchmarking Floquet Master Equations for Periodically Driven Open Quantum Systems

Konrad Mickiewicz, Valentin Link, Walter T. Strunz

The dynamics of open quantum systems is commonly described by quantum master equations derived under the assumption of weak system-bath coupling and a separation of timescales between system and bath. When the system is additionally subjected to a periodic driving, the validity of the resulting Floquet master equations is further restricted to regimes of weak or high-frequency driving. Here, we benchmark a set of commonly used Floquet master equations for a model of two locally driven spins coupled to a shared Ohmic reservoir at finite temperature. We systematically probe the accuracy of the equations as a function of the driving parameters, thus identifying limits of their applicability. Dynamical maps predicted by each master equation are compared against numerically exact non-Markovian simulations, tracking the full relaxation dynamics. We find that the accuracy of each master equation closely reflects the assumptions underlying its derivation. For the Floquet-Lindblad equation, errors can be strongly amplified near resonances where the secular approximation breaks down, while approaches that avoid the secular approximation perform better and exhibit a more systematic dependence of the error on driving frequency and amplitude.

quant-pharXiv:2606.06341•Jun 5, 2026•0 citations

High-Frequency Floquet Renormalization of Many-Body Dynamics: Suppression of Thermalization in a Prethermal Regime

Claudia Attaianese

This work presents a theoretical investigation of dynamic stabilization in interacting quantum many-body systems via high-frequency periodic driving. Using Floquet theory and the Magnus expansion, we derive the effective time-independent Hamiltonian governing the slow dynamics of a driven spin chain. We show that the external field induces a parametric renormalization of the transverse tunneling terms through a zeroth-order Bessel function dependence, leading to a critical drive amplitude at which transport is strongly suppressed. This suppression of the lowest-order hopping term gives rise to a long-lived prethermal regime in which many-body thermalization is significantly delayed. The resulting dynamics exhibit a sharp reduction in the short-to-intermediate time entanglement entropy growth rate. The framework is consistent with known results in Floquet engineering and coherent destruction of tunneling, and provides a unified interpretation of transport suppression and delayed scrambling in periodically driven systems. A falsifiable experimental protocol using ultracold atoms in optical lattices is proposed to validate the predicted threshold behavior and prethermal stabilization mechanism.

•Mar 23, 2026•0 citations
Floquet theory is an indispensable tool for analyzing periodically driven quantum many-body systems. Although it does not universally extend to classical systems, some of its methodologies can be adopted in the presence of well-separated timescales. Here we use these tools to investigate the stroboscopic behaviors of a classical spin chain that is driven by a periodic magnetic field and coupled to a thermal reservoir. We detail and expand our previous work: we investigate the significance of higher-order corrections to the classical Floquet-Magnus expansion in both the high- and low-frequency regimes; explicitly probe the evolution dynamics of the reservoir; and further explore how the driven system and the reservoir synchronize with the applied field at low frequencies. In line with our earlier results, we find that the high-frequency regime is characterized by a local Floquet-Gibbs ensemble with the reservoir acting as a nearly-reversible heat sink. At low frequencies, the driven system rapidly enters a synchronized state, which can only be fully described in a global picture accounting for the concurrent relaxation of the reservoir in a fictitious magnetic field arising from the drive. We highlight how the evolving nature of the reservoir may still be incorporated in a local picture by introducing an effective temperature. Finally, we show that generic local-dissipation models that account for the influence of the reservoir on the driven system phenomenologically through Markovian dissipative equations of motion can generally not reproduce the rich behavior that our microscopic simulations reveal. In particular, such models prove insufficient to account for the suppression of overall energy absorption that is induced by the here observed synchronization between driven system and reservoir.
Floquet theory is an indispensable tool for analysing periodically-driven quantum many-body systems. Although it does not universally extend to classical systems, some of its methodologies can be adopted in the presence of well-separated timescales. Here we use these tools to investigate the stroboscopic behaviours of a classical spin chain that is driven by a periodic magnetic field and coupled to a thermal reservoir. We detail and expand our previous work: we investigate the significance of higher-order corrections to the classical Floquet-Magnus expansion in both the high- and low-frequency regimes; explicitly probe the evolution the dynamics of the reservoir; and further explore how the driven system synchronises with the applied field at low frequencies. In line with our earlier results, we find that the high-frequency regime is characterised by a local Floquet-Gibbs ensemble with the reservoir acting as a nearly-reversible heatsink. At low frequencies, the driven system rapidly enters a synchronised state, which can only be fully described in a global picture accounting for the concurrent relaxation of the reservoir in a fictitious magnetic field arising from the drive. We highlight how the evolving nature of the reservoir may still be incorporated in a local picture by introducing an effective temperature. Finally, we argue that dissipative equations of motion for periodically-driven many-body systems, at least at intermediate frequencies, must generically be non-Markovian.
Exploiting the rich phenomenology of periodically driven many-body systems is notoriously hindered by persistent heating in both the classical and the quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir makes stabilization of a nontrivial steady state possible. To this end, we model both the system and the reservoir as classical spin chains where driving is applied through a rotating magnetic field, and we simulate the Hamiltonian dynamics of this setup. We find that the intuitive limits of infinite frequency and vanishing frequency, where the system dynamics is governed by the average and the instantaneous Hamiltonian, respectively, can be smoothly extended into entire regimes separated only by a small crossover region. At high frequencies, the driven system stroboscopically attains a Floquet-type Gibbs state at the reservoir temperature. At low frequencies, a global synchronized Gibbs state emerges, whose temperature may depart significantly from the initial temperature of the reservoir. Although our analysis in some parts relies on the specific properties of our setup, we argue that much of its phenomenology could be generic.
Exploiting the rich phenomenology of periodically-driven many-body systems is notoriously hindered by persistent heating in both the classical and quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir makes stabilisation of a non-trivial steady state possible. To this end, we model both the system and the reservoir as classical spin chains where driving is applied through a rotating magnetic field, and simulate the Hamiltonian dynamics of this setup. We find that the intuitive limits of infinite and vanishing frequency, where the system dynamics is governed by the average and the instantaneous Hamiltonian, respectively, can be smoothly extended into entire regimes separated only by a small crossover region. At high frequencies, the driven system stroboscopically attains a Floquet-type Gibbs state at the reservoir temperature. At low frequencies, a synchronised Gibbs state emerges, whose temperature may depart significantly from that of the reservoir. Although our analysis in some parts relies on the specific properties our setup, we argue that much of its phenomenology should be generic for a large class of systems.
It is proved that the energy absorption in a periodically driven classical spin system is exponentially slow in frequency, which results in a two-step relaxation called the Floquet prethermalization. This result is shown by establishing the classical limit of the quantum spin dynamics. The Floquet prethermal state is well described by the Gibbs ensemble with respect to the static effective Hamiltonian obtained by a truncation of the Floquet-Magnus expansion. On the other hand, the same effective Hamiltonian does not reproduce the local dynamics for an exponentially long time. This is due to the chaoticity of classical dynamics and in stark contrast to quantum spin systems, in which the effective Hamiltonian well reproduces the exact quantum dynamics up to an exponentially long time.
The dynamics of open quantum systems is commonly described by quantum master equations derived under the assumption of weak system-bath coupling and a separation of timescales between system and bath. When the system is additionally subjected to a periodic driving, the validity of the resulting Floquet master equations is further restricted to regimes of weak or high-frequency driving. Here, we benchmark a set of commonly used Floquet master equations for a model of two locally driven spins coupled to a shared Ohmic reservoir at finite temperature. We systematically probe the accuracy of the equations as a function of the driving parameters, thus identifying limits of their applicability. Dynamical maps predicted by each master equation are compared against numerically exact non-Markovian simulations, tracking the full relaxation dynamics. We find that the accuracy of each master equation closely reflects the assumptions underlying its derivation. For the Floquet-Lindblad equation, errors can be strongly amplified near resonances where the secular approximation breaks down, while approaches that avoid the secular approximation perform better and exhibit a more systematic dependence of the error on driving frequency and amplitude.
This work presents a theoretical investigation of dynamic stabilization in interacting quantum many-body systems via high-frequency periodic driving. Using Floquet theory and the Magnus expansion, we derive the effective time-independent Hamiltonian governing the slow dynamics of a driven spin chain. We show that the external field induces a parametric renormalization of the transverse tunneling terms through a zeroth-order Bessel function dependence, leading to a critical drive amplitude at which transport is strongly suppressed. This suppression of the lowest-order hopping term gives rise to a long-lived prethermal regime in which many-body thermalization is significantly delayed. The resulting dynamics exhibit a sharp reduction in the short-to-intermediate time entanglement entropy growth rate. The framework is consistent with known results in Floquet engineering and coherent destruction of tunneling, and provides a unified interpretation of transport suppression and delayed scrambling in periodically driven systems. A falsifiable experimental protocol using ultracold atoms in optical lattices is proposed to validate the predicted threshold behavior and prethermal stabilization mechanism.