The trace formula for a point scatterer on a hyperbolic surface with one cusp

2011/11/26 by Henrik Ueberschaer, Ueberschaer, Henrik
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1111.6198

34 pages. minor changes, added some details and minor changes of notation. arXiv admin note: text overlap with arXiv:1002.2930

arxiv created 2012/03/09 · arxiv updated 2012/03/12

Abstract

We prove an exact trace formula for the Laplacian with a delta potential - also known as a point scatterer - on a non-compact hyperbolic surface of finite volume with one cusp. Our formula is an analogue of the Selberg trace formula. We express the difference of perturbed and unperturbed trace as a smooth term plus a sum over combinations of diffractive orbits.

Citations

• The trace formula for singular perturbations of the Laplacian on hyperbolic surfaces

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