Semiclassical scaling of eigenstate thermalization in single-particle chaotic systems

Abstract:We study the off-diagonal matrix elements of real-space observables in time-reversal-invariant single-particle chaotic systems. By analyzing the semiclassical expression for the off-diagonal variance derived from Berry's conjecture, we show that the banded structure of the observable matrix emerges naturally. For local observables, we identify a characteristic bandwidth associated with a late-time timescale inversely proportional to the particle velocity. We further show that, for systems with steep-wall confinement, the predicted magnitude follows the entropy scaling of the eigenstate thermalization hypothesis (ETH), multiplied by an additional kinetic-energy-dependent factor that is independent of spatial dimension and is not captured by conventional many-body ETH. We illustrate these results through a case study of quantum billiards and verify the semiclassical scaling numerically in a generalized quarter-Sinai billiard. Our results elucidate the dynamical implications of Berry's conjecture and provide a comparison between single-particle eigenstate thermalization and many-body ETH.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Chaotic Dynamics (nlin.CD)

arXiv:2609.20052 [quant-ph]

(or arXiv:2609.20052v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.20052 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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