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Quantum Foundations

Characterization of Chaotic Evolution in Quantum Systems Induced by Random Hermitian Matrices

arXiv

Authors: Arkady Kurnosov, Sven Gnutzmann, Uzy Smilansky

Year

2026

Paper ID

76475

Status

Preprint

Abstract Read

~2 min

Abstract Words

100

Citations

N/A

Abstract

In a recent paper, a semiclassical Lyapunov exponent associated with a quantum Hamiltonian represented by a finite-dimensional Hermitian matrix was defined and placed on a mathematical foundation. The Lyapunov exponent characterizes the early stages of the evolution toward the ergodic state, while the late stages are characterized by the spectral gap of the corresponding Markov matrix. Here, we apply this formalism to five random-matrix ensembles. For each ensemble, we derive the mean Lyapunov exponent, its variance, and the spectral gap as functions of energy. We also present the corresponding thermal averages. Extensive numerical data are compared with the theoretical predictions.

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In a recent paper, a semiclassical Lyapunov exponent associated with a quantum Hamiltonian represented by a finite-dimensional Hermitian matrix was defined and placed on a...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2608.22571 [2] arXiv https://arxiv.org/abs/2608.22571 [3] Publisher https://arxiv.org/abs/2608.22571

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