The trace formula for a point scatterer on a compact hyperbolic surface
Mathematical Physics
2012-03-12 v2 math.MP
Quantum Physics
Abstract
An exact trace formula for the perturbation of the Laplacian by a Dirac delta potential on a compact hyperbolic Riemann surface is derived. The formula can be considered an analogue of the Selberg trace formula. The difference of perturbed and unperturbed trace is expressed as an identity term plus a sum over combinations of diffractive orbits which visit the position of the potential.
Keywords
Cite
@article{arxiv.1109.4329,
title = {The trace formula for a point scatterer on a compact hyperbolic surface},
author = {Henrik Ueberschaer},
journal= {arXiv preprint arXiv:1109.4329},
year = {2012}
}
Comments
32 pages; minor changes, fixed a mistake in the appendix