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.
arXiv commentThe 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"
References in corpus (22)
- A bound on chaos
- Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
- Comments on the Sachdev-Ye-Kitaev model
- Chaos and complexity by design
- Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
- Scrambling and entanglement spreading in long-range spin chains
- The Eigenstate Thermalization Hypothesis and Out of Time Order Correlators
- Positive quantum Lyapunov exponents in experimental systems with a regular classical limit
- Bounds on chaos from the eigenstate thermalization hypothesis
- Bridging entanglement dynamics and chaos in semiclassical systems
- Digital Quantum Simulation, Trotter Errors, and Quantum Chaos of the Kicked Top
- Effective Field Theory for Chaotic CFTs
- Eigenstate Thermalization Hypothesis and Free Probability
- Tripartite mutual information, entanglement, and scrambling in permutation symmetric systems with an application to quantum chaos
- Universal level statistics of the out-of-time-ordered operator
- Bound on the exponential growth rate of out-of-time-ordered correlators
- Quantum Lyapunov Spectrum
- Fine-Grained Chaos in Gravity
- Out-of-time-order fluctuation-dissipation theorem
- Quantum bounds and fluctuation-dissipation relations
- Subleading Bounds on Chaos
- Low temperature quantum bounds on simple models
Cited by in corpus (10)
- Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
- Measuring nonstabilizerness via multifractal flatness
- Refined quantum Lyapunov exponents from replica out-of-time-order correlators
- Quantum chaos without false positives
- Theory of robust quantum many-body scars in long-range interacting systems
- Designs via Free Probability
- Microcanonical windows on quantum operators
- Quantum Entropies and Decoherence for the Multiparticle Quantum Arnol'd Cat
- Controlling quantum chaos via Parrondo strategies on noisy intermediate-scale quantum hardware
- Behavior of correlation functions in the dynamics of the Multiparticle Quantum Arnol'd Cat