Fractional-power-law level statistics due to dynamical tunneling |
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Authors: | Bäcker Arnd Ketzmerick Roland Löck Steffen Mertig Normann |
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Institution: | Institut für Theoretische Physik, Technische Universit?t Dresden, 01062 Dresden, Germany. |
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Abstract: | 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(eff). |
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