Distribution of Eigenvalues for the Modular Group
E. Bogomolny, F. Leyvraz, C. Schmit
Abstract
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.
Create a lesson
Related papers
Chaotic eigenfunctions in phase space
S. Nonnenmacher, A. Voros
Improved control of delayed measured systems
Jens Christian Claussen, Heinz Georg Schuster
The accurate and comprehensive model of thin fluid flows with inertia on curved substrates
A. J. Roberts, Zhenquan Li
On periodic solutions of a Hamilton-Jacobi equation with periodic forcing
Andrei Sobolevskii
Drifters dispersion in the Adriatic Sea: Lagrangian data and chaotic model
Guglielmo Lacorata, Erik Aurell, Angelo Vulpiani
Generalized multibaker maps for open dissipative systems
Z. Kaufmann, P. Szépfalusy