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

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 ${\zeta }_0={\hslash }^2/D$. 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.

4 pages, submitted at Physical Review