On the Eigenvalue Spacing Distribution for a Point Scatterer on the Flat Torus
نویسندگان
چکیده
We study the level spacing distribution for the spectrum of a point scatterer on a flat torus. In the two-dimensional case, we show that in the weak coupling regime, the eigenvalue spacing distribution coincides with that of the spectrum of the Laplacian (ignoring multiplicities), by showing that the perturbed eigenvalues generically clump with the unperturbed ones on the scale of the mean level spacing. We also study the three dimensional case, where the situation is very different.
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