Quantum Surface of Section Method: Demonstration of semiclassical Berry-Robnik energy level spacing distribution in a generic 2-dim Hamiltonian system

Details Quantum Surface of Section Method: Demonstration of semiclassical Berry-Robnik energy level spacing distribution in a generic 2-dim Hamiltonian system Quantum Surface of Section Method: Demonstration of semiclassical Berry-Robnik energy level spacing distribution in a generic 2-dim Hamiltonian system

1995-02-08

arxiv.org/abs/chao-dyn/9502007v1

Nonlinear Sciences

Chaotic Dynamics

8 pages, file in plain LaTeX, 3 figures upon request submitted to J. Phys. A. Math. Gen. in Feb 1995

Scientific paper

10.1088/0305-4470/28/12/005

The recently developed quantum surface of section method is applied to a search for extremely high-lying energy levels in a simple but generic Hamiltonian system between integrability and chaos, namely the semiseparable 2-dim oscillator. Using the stretch of 13,445 consecutive levels with the sequential number around $1.8\cdot 10^7$ (eighteen million) we have clearly demonstrated the validity of the semiclassical Berry-Robnik level spacing distribution while at 1000 times smaller sequential quantum numbers we find the very persistent quasi universal phenomenon of power-law level repulsion which is globally very well described by the Brody distribution.

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