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.
%0 Journal Article
%1 PhysRevLett.127.050602
%A Mori, Takashi
%A Zhao, Hongzheng
%A Mintert, Florian
%A Knolle, Johannes
%A Moessner, Roderich
%D 2021
%I American Physical Society
%J Phys. Rev. Lett.
%K a
%N 5
%P 050602
%R 10.1103/PhysRevLett.127.050602
%T Rigorous bounds on the heating rate in Thue-Morse quasiperiodically and randomly driven quantum many-body systems
%U https://link.aps.org/doi/10.1103/PhysRevLett.127.050602
%V 127
%X 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.
@article{PhysRevLett.127.050602,
abstract = {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.},
added-at = {2023-11-16T13:49:48.000+0100},
author = {Mori, Takashi and Zhao, Hongzheng and Mintert, Florian and Knolle, Johannes and Moessner, Roderich},
biburl = {https://www.bibsonomy.org/bibtex/2d25567bdf96fb0065ed32eec7cfeec0c/ctqmat},
day = 30,
doi = {10.1103/PhysRevLett.127.050602},
interhash = {75c3b919ee713796af839cd524b0461f},
intrahash = {d25567bdf96fb0065ed32eec7cfeec0c},
journal = {Phys. Rev. Lett.},
keywords = {a},
month = {07},
number = 5,
numpages = {6},
pages = 050602,
publisher = {American Physical Society},
timestamp = {2023-11-16T13:49:48.000+0100},
title = {Rigorous bounds on the heating rate in Thue-Morse quasiperiodically and randomly driven quantum many-body systems},
url = {https://link.aps.org/doi/10.1103/PhysRevLett.127.050602},
volume = 127,
year = 2021
}