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Fractional-Power-Law Level-Statistics due to Dynamical Tunneling
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For systems with a mixed phase space we demonstrate that dynamical tunneling universally leads to a fractional power law of the level-spacing distribution P(s) over a wide range of small spacings s. Going beyond Berry-Robnik statistics, we take into account that dynamical tunneling rates between the regular and the chaotic region vary over many orders of magnitude. This results in a prediction of P(s) which excellently describes the spectral data of the standard map. Moreover, we show that the power-law exponent is proportional to the effective Planck constant h.
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Quantum chaos on the separatrix of the periodically perturbed Harper model
A quantum expression derived from the interaction-picture perturbation theory estimates the energy width of the chaotic separatrix layer in the periodically perturbed Harper model.
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