Related papers: Quantum bounds on the generalized Lyapunov exponents

Quantum bounds on the generalized Lyapunov exponents

URL: http://arxiv.org/abs/2212.10123v1
Date: Tue, 20 Dec 2022 09:46:32 GMT
Title: Quantum bounds on the generalized Lyapunov exponents
Authors: Silvia Pappalardi and Jorge Kurchan
Abstract summary: We discuss the generalized quantum Lyapunov exponents $L_q$, defined from the growth rate of the powers of the square commutator. We show that such exponents obey a generalized bound to chaos due to the fluctuation-dissipation theorem. Our findings are exemplified by a numerical study of the kicked top, a paradigmatic model of quantum chaos.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We discuss the generalized quantum Lyapunov exponents $L_q$, 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 $L_q$ 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 $q$ 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.

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