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Quantum surface-of-section method: Demonstration of semiclassical Berry-Robnik energy level-spacing distribution in a generic two-dimensional Hamiltonian system

1995; Institute of Physics; Volume: 28; Issue: 12 Linguagem: Inglês

10.1088/0305-4470/28/12/005

1361-6447

Tomaž Prosen,

Advanced Chemical Physics Studies

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 two-dimensional oscillator. Using the stretch of 13445 consecutive levels with the sequential number around 1.8*107 (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 phenomenological Brody distribution. This is the first statistically significant numerical confirmation of the Berry-Robnik surmise in an autonomous two-dimensional Hamiltonian system.