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

TL;DR

This paper shows that in systems with mixed phase space, dynamical tunneling causes a universal fractional power law in level-spacing distribution, with the exponent proportional to the effective Planck constant, improving spectral data modeling.

Contribution

It introduces a universal fractional power law for level-spacing due to dynamical tunneling, extending Berry-Robnik statistics by accounting for variable tunneling rates.

Findings

Power-law exponent proportional to effective Planck constant h

Spectral data of the standard map is well described by the new model

Dynamical tunneling universally affects level statistics in mixed systems

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.