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

arXiv:1509.05386 · Communications in Mathematical Physics

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

Dmitry A. Abanin, Wojciech De Roeck, Wen Wei Ho, François Huveneers

Published Jun 27, 2017• 300 citations
arXivHTMLPDF
DOI
10.1007/s00220-017-2930-x

Related papers

Many-body dynamics and prethermalization in interacting periodically driven systems

Ervand Kandelaki, Mark Spencer Rudner, Erez Berg +1 more

Bulletin of the American Physical Society•Mar 8, 2018•0 citations

Prethermalization and exponentially slow energy absorption in periodically driven many-body systems

Dmitry A. Abanin, Wen Wei Ho, Wojciech De Roeck +1 more

Bulletin of the American Physical Society•Mar 16, 2016•0 citations

Prethermalization and Conservation Laws in Quasi-Periodically Driven Quantum Systems

Matteo Gallone, Beatrice Langella

arXiv:2306.14022•Journal of Statistical Physics•Aug 10, 2024•6 citations

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems

Dmitry A. Abanin, Wojciech De Roeck, Wen Wei Ho +1 more

Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is exhibited for very long times. First, we consider quantum spin systems under periodic driving at high frequency ν. We prove that up to a quasi-exponential time τ∗∼ecνlog3ν, the system barely absorbs energy. Instead, there is an effective local Hamiltonian Dˆ that governs the time evolution up to τ∗, and hence this effective Hamiltonian is a conserved quantity up to τ∗. Next, we consider systems without driving, but with a separation of energy scales in the Hamiltonian. A prime example is the Fermi–Hubbard model where the interaction U is much larger than the hopping J. Also here we prove the emergence of an effective conserved quantity, different from the Hamiltonian, up to a time τ∗ that is (almost) exponential in U/J.

•Jan 1, 2017•270 citations

Rigorous Bounds on the Heating Rate in Thue-Morse Quasiperiodically and Randomly Driven Quantum Many-Body Systems

Takashi Mori, Hongzheng Zhao, Florian Mintert +2 more

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.

arXiv:2101.07065•Physical Review Letters•Jul 30, 2021•35 citations

Characterizations of prethermal states in periodically driven many-body systems with unbounded chaotic diffusion

Atanu Rajak, Itzhack Dana, Emanuele G. Dalla Torre

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.

arXiv:1905.00031•Physical review. B./Physical review. B•Sep 19, 2019•39 citations
Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is exhibited for very long times. First, we consider quantum spin systems under periodic driving at high frequency ν. We prove that up to a quasi-exponential time τ∗∼ecνlog3ν, the system barely absorbs energy. Instead, there is an effective local Hamiltonian Dˆ that governs the time evolution up to τ∗, and hence this effective Hamiltonian is a conserved quantity up to τ∗. Next, we consider systems without driving, but with a separation of energy scales in the Hamiltonian. A prime example is the Fermi–Hubbard model where the interaction U is much larger than the hopping J. Also here we prove the emergence of an effective conserved quantity, different from the Hamiltonian, up to a time τ∗ that is (almost) exponential in U/J.
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.
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.