Berry-Robnik level statistics in a smooth billiard system

TL;DR

This paper demonstrates the Berry-Robnik level spacing distribution in a generic quantized billiard system, revealing its validity at very small semi-classical parameters and showing a transition to Brody distribution at larger parameters.

Contribution

First demonstration of Berry-Robnik distribution in a generic billiard, analyzing its validity range and transition to Brody distribution with increasing semi-classical parameter.

Findings

Berry-Robnik distribution observed at small semi-classical parameters

Transition to Brody distribution with fractional power-law level repulsion

Distribution validity depends on the semi-classical parameter value

Abstract

Berry-Robnik level spacing distribution is demonstrated clearly in a generic quantized plane billiard for the first time. However, this ultimate semi-classical distribution is found to be valid only for extremely small semi-classical parameter (effective Planck's constant) where the assumption of statistical independence of regular and irregular levels is achieved. For sufficiently larger semiclassical parameter we find (fractional power-law) level repulsion with phenomenological Brody distribution providing an adequate global fit.