Parameter scaling in the decoherent quantum-classical transition for chaotic systems

Abstract

The quantum to classical transition has been shown to depend on a number of parameters. Key among these are a scale length for the action, $\hslash$, a measure of the coupling between a system and its environment, $D$, and, for chaotic systems, the classical Lyapunov exponent, $\lambda$. We propose computing a measure, reflecting the proximity of quantum and classical evolutions, as a multivariate function of $(\hslash ,\lambda ,D)$ and searching for transformations that collapse this hyper-surface into a function of a composite parameter $\zeta ={\hslash }^{\alpha }{\lambda }^{\beta }{D}^{\gamma }$. We report results for the quantum Cat Map, showing extremely accurate scaling behavior over a wide range of parameters and suggest that, in general, the technique may be effective in constructing universality classes in this transition.

Submitted

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