Quantum-classical correspondence on compact phase space

Details Quantum-classical correspondence on compact phase space Quantum-classical correspondence on compact phase space

2006-01-20

arxiv.org/abs/quant-ph/0601139v1

Physics

Quantum Physics

26 pages. 9 figures (31 .epz files), submitted to Nonlinearity

Scientific paper

10.1088/0951-7715/19/6/013

We propose to study the $L^2$-norm distance between classical and quantum phase space distributions, where for the latter we choose the Wigner function, as a global phase space indicator of quantum-classical correspondence. For example, this quantity should provide a key to understand the correspondence between quantum and classical Loschmidt echoes. We concentrate on fully chaotic systems with compact (finite) classical phase space. By means of numerical simulations and heuristic arguments we find that the quantum-classical fidelity stays at one up to Ehrenfest-type time scale, which is proportional to the logarithm of effective Planck constant, and decays exponentially with a maximal classical Lyapunov exponent, after that time.

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