On the Eigenvalue Spacing Distribution for a Point Scatterer on the Flat Torus

Zeév Rudnick; Henrik Ueberschär

doi:https://doi.org/10.1007/s00023-013-0241-0

On the Eigenvalue Spacing Distribution for a Point Scatterer on the Flat Torus

Zeév Rudnick, Henrik Ueberschär

School of Mathematical Sciences

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	1-27
Number of pages	27
Journal	Annales Henri Poincare
Volume	15
Issue number	1
DOIs	https://doi.org/10.1007/s00023-013-0241-0
State	Published - Jan 2014

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

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Cite this

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abstract = "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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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.

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On the Eigenvalue Spacing Distribution for a Point Scatterer on the Flat Torus

Abstract

All Science Journal Classification (ASJC) codes

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