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Paper detail

Distribution of Eigenvalues for the Modular Group

The two-point correlation function of energy levels for free motion on the modular domain, both with periodic and Dirichlet boundary conditions, are explicitly computed using a generalization of the Hardy-Littlewood method. It is shown that ion the limit of small separations they show an uncorrelated behaviour and agree with the Poisson distribution but they have prominent number-theoretical oscillations at larger scale. The results agree well with numerical simulations.

preprint1995arXivOpen access
E. BogomolnyF. LeyvrazC. Schmit
chao-dynnlin.CD
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E. BogomolnyF. LeyvrazC. Schmit

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