Second order perturbation theory for embedded eigenvalues
Mathematical Physics
2011-07-21 v1 math.MP
Spectral Theory
Abstract
We study second order perturbation theory for embedded eigenvalues of an abstract class of self-adjoint operators. Using an extension of the Mourre theory, under assumptions on the regularity of bound states with respect to a conjugate operator, we prove upper semicontinuity of the point spectrum and establish the Fermi Golden Rule criterion. Our results apply to massless Pauli-Fierz Hamiltonians for arbitrary coupling.
Cite
@article{arxiv.1006.5869,
title = {Second order perturbation theory for embedded eigenvalues},
author = {J. Faupin and J. S. Møller and E. Skibsted},
journal= {arXiv preprint arXiv:1006.5869},
year = {2011}
}
Comments
30 pages, 2 figures