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Fractional-Power-Law Level Statistics Due to Dynamical Tunneling

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Backer,  A.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Ketzmerick,  R.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Lock,  S.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Mertig,  N.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Backer, A., Ketzmerick, R., Lock, S., & Mertig, N. (2011). Fractional-Power-Law Level Statistics Due to Dynamical Tunneling. Physical Review Letters, 106(2): 024101.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-8DD5-D
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)