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

Dominique Delande (Laboratoire Kastler Brossel ENS; France); Jakub Zakrzewski; Karine Dupret; Paris

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

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arxiv chao-dyn/9501016 v1 pith:TU7V5LST submitted 1995-01-29 chao-dyn nlin.CD

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

Jakub Zakrzewski , Karine Dupret , Dominique Delande (Laboratoire Kastler Brossel ENS , Paris , France) This is my paper

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keywords chaoticenergylevelsmatrixpropertiesrandomstatesstatistical

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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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