Towards the Resolution of a Quantized Chaotic Phase-Space: The Interplay of Dynamics with Noise

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, which, 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.

Keywords

• quantum dissipation
• stochasticity
• nonlinearity
• chaos
• Wigner equation
• Fokker–Planck equation