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arXiv · 1007.4130

Fractional-Power-Law Level-Statistics due to Dynamical Tunneling

Arnd Bäcker·Roland Ketzmerick·Steffen Löck·Normann Mertig
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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.

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Arnd Bäcker, Roland Ketzmerick, Steffen Löck, Normann Mertig. 2011-02-01. Fractional-Power-Law Level-Statistics due to Dynamical Tunneling. https://doi.org/10.1103/physrevlett.106.024101

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