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Scars of symmetries in quantum chaos

1987; American Physical Society; Volume: 59; Issue: 16 Linguagem: Inglês

10.1103/physrevlett.59.1809

1092-0145

Dominique Delande, J. C. Gay,

Chaos control and synchronization

The hydrogen atom in a magnetic field is a classically chaotic Hamiltonian system. The energy-level fluctuations have been shown recently to obey a random-matrix model. Here we go beyond the statistical analysis by studying the destruction of the low-field dynamical symmetries. We especially establish the existence of scars of symmetries in the chaotic regime. The symmetry properties are no longer associated with one given level, but fractalized onto clusters of levels, generating a long-range order.