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

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

2002-06-11

arxiv.org/abs/quant-ph/0206069v1

Physics

Quantum Physics

Submitted

Scientific paper

10.1103/PhysRevLett.90.014103

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, $\hbar$, 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 $(\hbar,\lambda,D)$ and searching for transformations that collapse this hyper-surface into a function of a composite parameter $\zeta = \hbar^{\alpha}\lambda^{\beta}D^{\gamma}$. 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.

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