Chaos and Lyapunov exponents in classical and quantal distribution dynamics

Abstract

We analytically establish the role of a spectrum of Lyapunov exponents in the evolution of phase-space distributions $\rho (p,q)$. Of particular interest is ${\lambda }_2$, an exponent which quantifies the rate at which chaotically evolving distributions acquire structure at increasingly smaller scales and which is generally larger than the maximal Lyapunov exponent $\lambda$ for trajectories. The approach is trajectory-independent and is therefore applicable to both classical and quantum mechanics. In the latter case we show that the $\hslash \to 0$ limit yields the classical, fully chaotic, result for the quantum cat map.

5 RevTeX pages + 2 ps figs. Phys. Rev. E (to appear,'97)

Cited by in corpus (28)

• Entanglement production in coupled chaotic systems : Case of the Kicked Tops
• Lyapunov exponent in quantum mechanics. A phase-space approach
• Lyapunov exponents, entropy production and decoherence
• Quantum biology on the edge of quantum chaos
• Information geometric methods for complexity
• How complex is the quantum motion?
• Exponentially rapid decoherence of quantum chaotic systems
• Environmental effects in the quantum-classical transition for the delta-kicked harmonic oscillator
• Parameter scaling in the decoherent quantum-classical transition for chaotic systems
• The production rate of the coarse grained Gibbs entropy and the Kolmogorov-Sinai entropy: a real connection ?
• Complexity of Quantum States and Reversibility of Quantum Motion
• Chaos and Quantum-Classical Correspondence via Phase Space Distribution Functions
• Statistical and dynamical properties of the quantum triangle map
• Complexity of quantum motion and quantum-classical correspondence: A phase-space approach
• Trajectory versus probability density entropy
• Quantum Measurement and Entropy Production
• Wigner separability entropy and complexity of quantum dynamics
• Phase-space characterization of complexity in quantum many-body dynamics
• Chaos and Correspondence in Classical and Quantum Hamiltonian Ratchets: A Heisenberg Approach
• Complexity and instability of quantum motion near a quantum phase transition
• Temperature crossover of decoherence rates in chaotic and regular bath dynamics
• Quantum-classical correspondence on compact phase space
• Quantum Dynamics Against a Noisy Background
• How Well a Chaotic Quantum System Can Retain Memory of Its Initial State?
• Entanglement dynamics and classical complexity
• Quantum-classical entropy analysis for nonlinearly-coupled continuous-variable bipartite systems
• Quantum Liang Information Flow Probe of Causality across Critical Points
• Separability and entanglement in classical eigenfunctions as a criterion for Hamiltonian chaos