Classical versus Quantum Time Evolution of Densities at Limited Phase-Space Resolution

Abstract

We study the interrelations between the classical (Frobenius-Perron) and the quantum (Husimi) propagator for phase-space (quasi-)probability densities in a Hamiltonian system displaying a mix of regular and chaotic behavior. We focus on common resonances of these operators which we determine by blurring phase-space resolution. We demonstrate that classical and quantum time evolution look alike if observed with a resolution much coarser than a Planck cell and explain how this similarity arises for the propagators as well as their spectra. The indistinguishability of blurred quantum and classical evolution implies that classical resonances can conveniently be determined from quantum mechanics and in turn become effective for decay rates of quantum correlations.

10 pages, 3 figures

References in corpus (1)

• Resonances of the Frobenius-Perron Operator for a Hamiltonian Map with a Mixed Phase Space

Cited by in corpus (21)

• Large N classical dynamics of holographic matrix models
• Universal Long-time Behavior of Nuclear Spin Decays in a Solid
• Classical decays in decoherent quantum maps
• On the long-time behavior of spin echo and its relation to free induction decay
• Spectral properties of noisy classical and quantum propagators
• Dissipation time and decay of correlations
• Sigma models for quantum chaotic dynamics
• Spectral properties and classical decays in quantum open systems
• Noise models for superoperators in the chord representation
• Propagating wave correlations in complex systems
• Classical approach to equilibrium of out-of-time ordered correlators in mixed systems
• Semiclassical Formulae For Wigner Distributions
• Theory of Irreversibility in Quantum Many-Body Systems
• Det-Det Correlations for Quantum Maps: Dual Pair and Saddle-Point Analyses
• Phase relationship between the long-time beats of free induction decays and spin echoes in solids
• Local random vector model for semiclassical fractal structure of chaotic resonance states
• Quantization of Classical Maps with tunable Ruelle-Pollicott Resonances
• Classical projected phase space density of billiards and its relation to the quantum Neumann spectrum
• Ruelle-Pollicott Decay of Out-of-Time-Order Correlators in Many-Body Systems
• Relaxation Time of Quantized Toral Maps
• Coarse Grained Liouville Dynamics of piecewise linear discontinuous maps