Distribution of eigenvalues for the modular group |
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| Authors: | E. Bogomolny F. Leyvraz C. Schmit |
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| Affiliation: | (1) Division de Physique Théorique, Unité de Recherche des Université Paris 11 et Paris 6, Associée au CNRS, Institut de Physique Nucléaire, F-91406 Orsay Cedex, France;(2) Present address: L.D. Landau Institute of Theoretical Physics, 142432 Cherogolovka, Russia;(3) Present address: Instituto de Física, University of Mexico, Apdo. postal 20-364, 01000 Mexico City, Mexico |
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| Abstract: | The two-point correlation functions 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 in 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. |
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