Quantum Bounds on the Generalized Lyapunov Exponents

  title={Quantum Bounds on the Generalized Lyapunov Exponents},
  author={Silvia Pappalardi and Jorge Kurchan},
We discuss the generalized quantum Lyapunov exponents Lq, 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 Lq 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… 

Figures from this paper

Thermal quenching of classical and semiclassical chaos

The growth rate of out-of-time ordered correlators (OTOCs) provide for the notion of a quantum Lyapunov exponent, which quantifies chaos and information scrambling in quantum systems. In thermal

Microcanonical windows on quantum operators

We discuss a construction of a microcanonical projection WOW of a quantum operator O, its spectrum, and the retrieval of canonical many-time correlations from it.

Quantum Lyapunov spectrum

A bstractWe introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production. Our

Low temperature quantum bounds on simple models

In the past few years, there has been considerable activity around a set of quantum bounds on transport coefficients (viscosity) and chaos (Lyapunov exponent), relevant at low temperatures. The

Generalized Lyapunov exponents in high-dimensional chaotic dynamics and products of large random matrices

We study the behavior of the generalized Lyapunov exponents for chaotic symplectic dynamical systems and products of random matrices in the limit of large dimensionsD. For products of random matrices

Positive quantum Lyapunov exponents in experimental systems with a regular classical limit.

It is shown that for experimentally accessible parameters, OTOCs can grow exponentially also when the Dicke model is in the regular regime, and the same holds for the Lipkin-Meshkov-Glick model, which is integrable and also experimentally realizable.

Quantum Bound to Chaos and the Semiclassical Limit

We discuss the quantum bound on chaos in the context of the free propagation of a particle in an arbitrarily curved surface at low temperatures. The semiclassical calculation of the Lyapunov exponent

A bound on chaos

A bstractWe conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation

Quantum bounds and fluctuation-dissipation relations

In recent years, there has been intense attention on the constraints posed by quantum mechanics on the dynamics of the correlation at low temperatures, triggered by the postulation and derivation of

Bridging entanglement dynamics and chaos in semiclassical systems

It is widely recognized that entanglement generation and dynamical chaos are intimately related in semiclassical models via the process of decoherence. In this paper, we propose a unifying framework

Classical and quantum chaos for a kicked top

We discuss a top undergoing constant precession around a magnetic field and suffering a periodic sequence of impulsive nonlinear kicks. The squared angular momentum being a constant of the motion the

Quantum signatures of chaos

The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2,