Scaling laws in the quantum to classical transition in chaotic systems

Details Scaling laws in the quantum to classical transition in chaotic systems Scaling laws in the quantum to classical transition in chaotic systems

2008-10-31

arxiv.org/abs/0810.5740v1

Phys. Rev. E 79, 02520 R (2009)

Physics

Quantum Physics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevE.79.025203

We study the quantum to classical transition in a chaotic system surrounded by a diffusive environment. The emergence of classicality is monitored by the Renyi entropy, a measure of the entanglement of a system with its environment. We show that the Renyi entropy has a transition from quantum to classical behavior that scales with $\hbar^2_{\rm eff}/D$, where $\hbar_{\rm eff}$ is the effective Planck constant and $D$ is the strength of the noise. However, it was recently shown that a different scaling law controls the quantum to classical transition when it is measured comparing the corresponding phase space distributions. We discuss here the meaning of both scalings in the precise definition of a frontier between the classical and quantum behavior. We also show that there are quantum coherences that the Renyi entropy is unable to detect which questions its use in the studies of decoherence.

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