Positive commutators, Fermi golden rule and the spectrum of zero temperature Pauli-Fierz Hamiltonians
Abstract
Description
We perform the spectral analysis of a zero temperature Pauli-Fierz system for small coupling constants. Under the hypothesis of Fermi golden rule, we show that the embedded eigenvalues of the uncoupled system disappear and establish a limiting absorption principle above this level of energy. We rely on a positive commutator approach introduced by Skibsted and pursued by Georgescu-Gerard-Moller. We complete some results obtained so far by Derezinski-Jaksic on one side and by Bach-Froehlich-Segal-Soffer on the other side.
28 pages. References added and few typos corrected
28 pages. References added and few typos corrected