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Related Experiment Video

Updated: Jun 20, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Operator-Weyl-symbol approach to eigenstate thermalization hypothesis.

Xiao Wang^1,2,3, Wen-Ge Wang^2,3,4

¹University of Science and Technology of China, Wilczek Quantum Center, Shanghai Institute for Advanced Studies, Shanghai 201315, China.

Physical Review. E

|June 19, 2026

Summary

This study develops a semiclassical theory for quantum thermalization, revealing that the thermalization timescale depends inversely on the Hamiltonian

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Last Updated: Jun 20, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

Quantum mechanics
Statistical mechanics
Condensed matter physics

Background:

The eigenstate thermalization hypothesis (ETH) describes how isolated quantum systems thermalize.
Off-diagonal elements of observables in the energy basis are crucial for understanding ETH.
A semiclassical approach can provide insights into quantum phenomena.

Purpose of the Study:

To develop a semiclassical theory for the off-diagonal function in ETH.
To analytically determine the scaling properties of off-diagonal matrix elements.
To connect quantum thermalization timescales with classical properties.

Main Methods:

Employing Weyl symbols for operators to construct a semiclassical theory.
Analytical derivation of the structure and bandwidth of the observable matrix.
Numerical verification using the Lipkin-Meshkov-Glick model.

Main Results:

The observable matrix exhibits a banded structure with a bandwidth scaling linearly with Planck's constant (ℏ).
The bandwidth also depends on the phase-space gradient of the classical Hamiltonian and the observable.
A scaling of ρ_{dos}^{-1/2} for the off-diagonal function is explained.
Thermalization timescale is predicted to be inversely proportional to the Hamiltonian's phase-space gradient.

Conclusions:

The developed semiclassical theory successfully explains features of the off-diagonal function in ETH.
The findings provide a link between quantum thermalization and classical system properties.
The study offers a new perspective on the dynamics of quantum thermalization.