Parameter scaling in a novel measure of quantum-classical difference for decohering chaotic systems

TL;DR

This paper introduces a new measure for quantum-classical differences in open quantum systems, demonstrating precise scaling behavior in a driven Duffing oscillator and revealing saturation effects in the quantum-classical difference.

Contribution

The paper presents a novel diagnostic for quantum-classical differences and uncovers its scaling properties in chaotic systems, advancing understanding of quantum-classical transition mechanisms.

Findings

The measure shows precise scaling with the parameter ζ₀ over long times.

Dynamics follow a similar pattern regardless of ζ₀, with curves collapsing when scaled.

Quantum-classical difference saturates at both small and large ζ₀ values.

Abstract

In this paper we introduce a diagnostic for measuring the quantum-classical difference for open quantum systems, which is the normalized size of the quantum terms in the Master equation for Wigner function evolution. For a driven Duffing oscillator, this measure shows remarkably precise scaling over long time-scales with the parameter $\zeta_0=\hbar^2/D$. We also see that, independent of $\zeta_0$ the dynamics follows a similar pattern. For small $\zeta_0$ all of our curves collapses to essentially a single curve when scaled by the maximum value of the quantum-classical difference. In both limits of large and small $\zeta_0$ we see a saturation effect in the size of the quantum-classical difference; that is, the instantaneous difference between quantum and classical evolutions cannot be either too small or too large.