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

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

2009-04-21

arxiv.org/abs/0904.3353v1

Physics

Quantum Physics

4 pages, submitted at Physical Review

Scientific paper

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.

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