spectrum of zero temperature Pauli_Fierz Hamiltonians

摘要

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_Gérard_M_ller. We complete some results obtained so far by Derezi_ski_Jak_i_ on one side and by Bach_Fr_hlich_Sigal_Soffer on the other side.