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

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

2010-07-23

arxiv.org/abs/1007.4130v2

Phys. Rev. Lett. 106, 024101 (2011)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.106.024101

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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