Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner

Details Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner

1995-01-29

arxiv.org/abs/chao-dyn/9501016v1

Phys. Rev. Lett. 74, 522 (1995)

Nonlinear Sciences

Chaotic Dynamics

10 pages, Revtex 3.0 + 4 .ps figures tar-compressed using uufiles package, use csh to unpack (on Unix machine), to be publishe

Scientific paper

10.1103/PhysRevLett.74.522

For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom in a magnetic field and the quartic oscillator - which display nearest neighbor statistics strongly different from the usual Wigner distribution. We interpret the results with a simple model using a set of regular states coupled to a set of chaotic states modeled by a random matrix.

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