Conditions for the Quantum to Classical Transition: Trajectories vs. Phase Space Distributions

Abstract

We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong'' transition) [Bhattacharya, et al., Phys. Rev. Lett. 85: 4852 (2000)], and the second by considering phase-space densities (the ``weak'' transition) [Greenbaum, et al., Chaos 15, 033302 (2005)]. On the face of it these conditions appear rather different. We show, however, that in the semiclassical regime, in which the action of the system is large compared to $\hslash$, and the measurement noise is small, they both offer an essentially equivalent local picture. Within this regime, the weak conditions dominate while in the opposite regime where the action is not much larger than Planck's constant, the strong conditions dominate.

8 pages, 2 eps figures

References in corpus (14)

• A Straightforward Introduction to Continuous Quantum Measurement
• A simple model of quantum trajectories
• Decoherence, Chaos, and the Correspondence Principle
• Continuous Quantum Measurement and the Emergence of Classical Chaos
• Information, disturbance and Hamiltonian quantum feedback control
• Quantum state diffusion, localization and computation
• Quantum chaos in open systems: a quantum state diffusion analysis
• The Quantum-Classical Transition in Nonlinear Dynamical Systems
• Continuous Quantum Measurement and the Quantum to Classical Transition
• The transition to classical chaos in a coupled quantum system through continuous measurement
• Parameter scaling in the decoherent quantum-classical transition for chaotic systems
• Recovering classical dynamics from coupled quantum systems through continuous measurement
• Persistent Entanglement in the Classical Limit
• Entanglement vs. the quantum-to-classical transition