Consequences of Flooding on Spectral Statistics

Details Consequences of Flooding on Spectral Statistics Consequences of Flooding on Spectral Statistics

2012-01-20

arxiv.org/abs/1201.4288v2

Phys. Rev. E 85, 036213 (2012)

Nonlinear Sciences

Chaotic Dynamics

9 pages, 5 figures

Scientific paper

10.1103/PhysRevE.85.036213

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.

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