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Thermalization time in many-body quantum systems.

Léa Ferreira dos Santos, Eduardo Jonathan Torres-Herrera, Francisco Pérez-Bernal, Talía L. M. Lezama, Yevgeny Bar Lev

Published Feb 23, 2021• 0 citations
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A profound quest of statistical mechanics is the origin of irreversibility - the arrow of time. New stimulants have been provided, thanks to unprecedented degree of control reached in experiments with isolated quantum systems and rapid theoretical developments of manybody localization in disordered interacting systems. The proposal of (many-body) eigenstate thermalization (ET) for these systems reinforces the common belief that either interaction or extrinsic randomness is required for thermalization. Here, we unveil a quantum thermalization mechanism challenging this belief. We find that, provided one-body quantum chaos is present, as a pure many-body state evolves the arrow of time can emerge, even without interaction or randomness. In times much larger than the Ehrenfest time that signals the breakdown of quantum-classical correspondence, quantum chaotic motion leads to thermal [Fermi-Dirac (FD) or Bose-Einstein (BE)] distributions and thermodynamics in individual eigenstates. Our findings lay dynamical foundation of statistical mechanics and thermodynamics of isolated quantum systems.

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An explanation of the thermalization of closed quantum systems is the eigenstate thermalization hypothesis, which states that all eigenstates are thermal. Quantum many-body scars are a relatively newly discovered phenomenon, which describe a band of nonthermal eigenstates that have high overlap with the initial state. These states impede the thermalization of systems. This paper looks at a system of ultracold Rubidium Rydberg atoms that interact via dipole-dipole interactions. This system has apparently normal thermalization when the dipole interactions are primarily two-body interactions, however when they are primarily three-body interaction the system thermalizes slower than expected. Simulations results are presented which suggest that scars states affect the time evolution of the system.

•May 15, 2026•0 citations
A profound quest of statistical mechanics is the origin of irreversibility - the arrow of time. New stimulants have been provided, thanks to unprecedented degree of control reached in experiments with isolated quantum systems and rapid theoretical developments of manybody localization in disordered interacting systems. The proposal of (many-body) eigenstate thermalization (ET) for these systems reinforces the common belief that either interaction or extrinsic randomness is required for thermalization. Here, we unveil a quantum thermalization mechanism challenging this belief. We find that, provided one-body quantum chaos is present, as a pure many-body state evolves the arrow of time can emerge, even without interaction or randomness. In times much larger than the Ehrenfest time that signals the breakdown of quantum-classical correspondence, quantum chaotic motion leads to thermal [Fermi-Dirac (FD) or Bose-Einstein (BE)] distributions and thermodynamics in individual eigenstates. Our findings lay dynamical foundation of statistical mechanics and thermodynamics of isolated quantum systems.
We develop a rigorous system-agnostic method to predict quantum thermalization in an overwhelming fraction of accessible pure states in a many-body system, entirely in terms of certain out-of-time-ordered correlators of few-body observables. In contrast to previous rigorous results on thermalization with semiclassical counterparts, our method is not limited to statistical averages of observables, such as time averages in ergodicity or state averages in mixing. Moreover, consistent with such approaches, we retain the advantage of not requiring a detailed knowledge of energy eigenstate structure or thermodynamically large times, which can become intractable for systems with more than a handful of particles. Our approach is centered on a geometric result that connects thermalization to the alignment of high dimensional subspaces in a Hilbert space, which is determined by the saturation of "controllably nonlocal" out-of-time-ordered correlators. We discuss the possibility of predicting quantum thermalization in almost all states at almost all times from finite-time observations of a single such correlator per observable. This formalism reduces the problem of establishing pure state quantum thermalization at finite times in almost all complex many-body states to a theoretically or experimentally accessible study of few-body correlators, even in thermodynamically large systems.
An explanation of the thermalization of closed quantum systems is the eigenstate thermalization hypothesis, which states that all eigenstates are thermal. Quantum many-body scars are a relatively newly discovered phenomenon, which describe a band of nonthermal eigenstates that have high overlap with the initial state. These states impede the thermalization of systems. This paper looks at a system of ultracold Rubidium Rydberg atoms that interact via dipole-dipole interactions. This system has apparently normal thermalization when the dipole interactions are primarily two-body interactions, however when they are primarily three-body interaction the system thermalizes slower than expected. Simulations results are presented which suggest that scars states affect the time evolution of the system.