Consequences of Flooding on Spectral Statistics

TL;DR

This paper investigates how flooding, caused by increased regular-to-chaotic couplings, leads to a transition in spectral statistics from Berry-Robnik to Wigner distributions in systems with mixed phase space, supported by a new improved distribution model.

Contribution

The authors introduce a flooding-improved Berry-Robnik distribution accounting for regular state disappearance and extend it to include tunneling effects, accurately modeling spectral statistics transitions.

Findings

Transition from Berry-Robnik to Wigner distribution observed

Flooding effect reduces effective size of regular islands

Flooding- and tunneling-improved distribution matches numerical data

Abstract

We study spectral statistics in systems with a mixed phase space, in which regions of regular and chaotic motion coexist. Increasing their density of states, we observe a transition of the level-spacing distribution P(s) from Berry-Robnik to Wigner statistics, although the underlying classical phase-space structure and the effective Planck constant remain unchanged. This transition is induced by flooding, i.e., the disappearance of regular states due to increasing regular-to-chaotic couplings. We account for this effect by a flooding-improved Berry-Robnik distribution, in which an effectively reduced size of the regular island enters. To additionally describe power-law level repulsion at small spacings, we extend this prediction by explicitly considering the tunneling couplings between regular and chaotic states. This results in a flooding- and tunneling-improved Berry-Robnik distribution which is in excellent agreement with numerical data.