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Authors: For systems with a mixed phase space we demonstrate that dynamical tunneling universally leads to a fractional power-law of the nearest-neighbor level-spacing distribution $P(s)$ at 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 the level-spacing distribution which excellently describes the spectral data of the standard map. Moreover, we show that the fractional power-law exponent is proportional to the effective Planck constant $h$ and discuss the emergence of Berry-Robnik statistics in the semiclassical limit $h \to 0$. |
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