Distribution of Eigenvalues for the Modular Group

C. Schmit (Division de Physique Th\'eorique; E. Bogomolny (Division de Physique Th\'eorique; F. Leyvraz (Instituto de F\'isica; France); Institut de Physique Nucl\'eaire; Mexico City); Orsay; University of Mexico

arxiv: chao-dyn/9509019 · v1 · pith:JM6UYDJMnew · submitted 1995-09-26 · chao-dyn · nlin.CD

Distribution of Eigenvalues for the Modular Group

E. Bogomolny (Division de Physique Th\'eorique , Institut de Physique Nucl\'eaire , Orsay , France) , F. Leyvraz (Instituto de F\'isica , University of Mexico , Mexico City) , C. Schmit (Division de Physique Th\'eorique This is my paper

classification chao-dyn nlin.CD

keywords agreedistributionmodulartheybehaviourboundarycomputedconditions

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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.

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Distribution of Eigenvalues for the Modular Group

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