Quantum bounds on the generalized Lyapunov exponents
arXiv:2212.10123 · doi:10.3390/e25020246
Abstract
We discuss the generalized quantum Lyapunov exponents , defined from the growth rate of the powers of the square commutator. They may be related to an appropriately defined thermodynamic limit of the spectrum of the commutator, which plays the role of a large deviation function, obtained from the exponents via a Legendre transform. We show that such exponents obey a generalized bound to chaos due to the fluctuation-dissipation theorem, as already discussed in the literature. The bounds for larger are actually stronger, placing a limit on the large deviations of chaotic properties. Our findings at infinite temperature are exemplified by a numerical study of the kicked top, a paradigmatic model of quantum chaos.
The paper is dedicated to Professor Giulio Casati on the Occasion of his 80th Birthday, submitted to the Special Issue of Entropy: "Quantum chaos - dedicated to Professor Giulio Casati on the Occasion of His 80th Birthday"
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