Thermalization rates and quantum Ruelle-Pollicott resonances: Insights from operator hydrodynamics
- 1Harvard University
- 2Purdue University, West Lafayette
- 3King’s College London
Abstract
In thermalizing many-body quantum systems without conservation laws, such as ergodic Floquet and random unitary circuits, local expectation values are predicted to decay to their equilibrium values exponentially quickly. In this work, we derive a relationship between said exponential decay rate g ¯ and the operator spreading properties of a local unitary evolution. A hydrodynamical picture for operator spreading allows us to argue that, for random unitary circuits, g ¯ is encoded by the leading eigenvalue of a dynamical map obtained by enriching unitary dynamics with dissipation, in the limit of weak dissipation. We argue that the size of the eigenvalue does not depend on the details of this weak dissipation (given mild assumptions on properties of the ergodic dynamics), so long as it only suppresses large operators significantly. Our calculations are based on analytical results for random unitary circuits, but we argue that similar results hold for ergodic Floquet systems. These conjectures are in accordance with existing results that numerically obtain quantum many-body analogs of classical Ruelle-Pollicott resonances [Prosen, ; Mori, ] by studying unitary evolutions subject to weak dissipation.
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BibTeX
@article{zhang2026thermalization,
title = {{Thermalization rates and quantum Ruelle-Pollicott resonances: Insights from operator hydrodynamics}},
author = {Carolyn Zhang and Laimei Nie and Curt W. von Keyserlingk},
journal = {Physical Review Research},
year = {2026},
month = jun,
doi = {10.1103/r8qy-dcgq},
url = {https://doi.org/10.1103/r8qy-dcgq},
note = {CC BY},
}
RIS
TY - JOUR
TI - Thermalization rates and quantum Ruelle-Pollicott resonances: Insights from operator hydrodynamics
AU - Carolyn Zhang
AU - Laimei Nie
AU - Curt W. von Keyserlingk
PY - 2026
DA - 2026/06/10
JO - Physical Review Research
DO - 10.1103/r8qy-dcgq
UR - https://doi.org/10.1103/r8qy-dcgq
AB - In thermalizing many-body quantum systems without conservation laws, such as ergodic Floquet and random unitary circuits, local expectation values are predicted to decay to their equilibrium values exponentially quickly. In this work, we derive a relationship between said exponential decay rate g ¯ and the operator spreading properties of a local unitary evolution. A hydrodynamical picture for operator spreading allows us to argue that, for random unitary circuits, g ¯ is encoded by the leading eigenvalue of a dynamical map obtained by enriching unitary dynamics with dissipation, in the limit of weak dissipation. We argue that the size of the eigenvalue does not depend on the details of this weak dissipation (given mild assumptions on properties of the ergodic dynamics), so long as it only suppresses large operators significantly. Our calculations are based on analytical results for random unitary circuits, but we argue that similar results hold for ergodic Floquet systems. These conjectures are in accordance with existing results that numerically obtain quantum many-body analogs of classical Ruelle-Pollicott resonances [Prosen, ; Mori, ] by studying unitary evolutions subject to weak dissipation.
SN - 2643-1564
ER -