Towards the resolution of a quantized chaotic phase space: The interplay of dynamics with noise

TL;DR

This paper explores the analogy between quantum dynamics of open systems and classical systems with noise, suggesting a finite resolution for quantized state space especially in chaotic regimes, using the dissipative Wigner equation.

Contribution

It introduces a formal analogy between quantum open system dynamics and classical noisy systems, proposing a finite resolution for quantized phase space beyond the Planck scale.

Findings

Finite resolution of quantized state space suggested for chaotic systems.

Dissipative Wigner equation parallels classical Fokker-Planck dynamics.

Examples include noisy Hopf cycles and Van der Pol oscillators.

Abstract

We outline formal and physical similarities between the quantum dynamics of open systems, and the mesoscopic description of classical systems affected by weak noise. The main tool of our interest is the dissipative Wigner equation, that, for suitable timescales, becomes analogous to the Fokker-Planck equation describing classical advection and diffusion. This correspondence allows in principle to surmise a finite resolution, other than the Planck scale, for the quantized state space of the open system, particularly meaningful when the latter underlies chaotic classical dynamics. We provide representative examples of the quantum-stochastic parallel with noisy Hopf cycles and Van der Pol type oscillators.