Quantum-Classical Correspondence via Liouville Dynamics: II. Correspondence for Chaotic Hamiltonian Systems

Abstract

We prove quantum-classical correspondence for bound conservative classically chaotic Hamiltonian systems. In particular, quantum Liouville spectral projection operators and spectral densities, and hence classical dynamics, are shown to approach their classical analogs in the $h\to 0$ limit. Correspondence is shown to occur via the elimination of essential singularities. In addition, applications to matrix elements of observables in chaotic systems are discussed.

41 pages, revtex, second of two papers

References in corpus (3)

• Exponential Divergence and Long Time Relaxation in Chaotic Quantum Dynamics
• A Semiclassical Calculation of Scars for a Smooth Potential
• Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation

Cited by in corpus (27)

• Operational Dynamic Modeling Transcending Quantum and Classical Mechanics
• The Born Rule in Quantum and Classical Mechanics
• Wigner phase space distribution as a wave function
• Intrinsic Decoherence Dynamics in Smooth Hamiltonian Systems: Quantum-classical Correspondence
• Suppression of decoherence via strong intra-environmental coupling
• Efficient method to generate time evolution of the Wigner function for open quantum systems
• Aspects of nonlocality from a quantum trajectory perspective: A WKB approach to Bohmian mechanics
• When is Quantum Decoherence Dynamics Classical?
• Minimum requirements for laser-induced symmetry breaking in quantum and classical mechanics
• Phase Space Correspondence between Classical Optics and Quantum Mechanics
• Quantum-classical correspondence in the vicinity of periodic orbits
• Chaos and Quantum-Classical Correspondence via Phase Space Distribution Functions
• Decoherence Effects in Reactive Scattering
• Equilibrium Coherence in the Multi-level Spin-boson Model
• Chaos and Correspondence in Classical and Quantum Hamiltonian Ratchets: A Heisenberg Approach
• Classical-Wigner Phase Space Approximation to Cumulative Matrix Elements in Coherent Control
• The wave operator representation of quantum and classical dynamics
• Quantum Kicked Dynamics and Classical Diffusion
• Kraus decomposition for chaotic environments
• Temperature crossover of decoherence rates in chaotic and regular bath dynamics
• Kraus decomposition for chaotic environments including time-dependent subsystem Hamiltonians
• Quantum pathology of static internal imperfections in flawed quantum computers
• The Schwinger action principle for classical systems
• Operational classical mechanics: Holonomic Systems
• Semiclassical Dynamics in Wigner Phase Space I : Adiabatic Hybrid Wigner Dynamics
• Duality between quantum and classical dynamics for integrable billiards
• Separability and entanglement in classical eigenfunctions as a criterion for Hamiltonian chaos