TY - JOUR
T1 - On the Eigenvalue Spacing Distribution for a Point Scatterer on the Flat Torus
AU - Rudnick, Zeév
AU - Ueberschär, Henrik
N1 - Funding Information:
The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement no 320755. H.U. was supported by a Minerva Fellowship.
PY - 2014/1
Y1 - 2014/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84891561175&partnerID=8YFLogxK
U2 - 10.1007/s00023-013-0241-0
DO - 10.1007/s00023-013-0241-0
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AN - SCOPUS:84891561175
SN - 1424-0637
VL - 15
SP - 1
EP - 27
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 1
ER -