Positive commutators, Fermi golden rule and the spectrum of zero temperature Pauli-Fierz Hamiltonians

Details Positive commutators, Fermi golden rule and the spectrum of zero temperature Pauli-Fierz Hamiltonians Positive commutators, Fermi golden rule and the spectrum of zero temperature Pauli-Fierz Hamiltonians

2008-06-24

arxiv.org/abs/0806.3992v2

Physics

Mathematical Physics

28 pages. References added and few typos corrected

Scientific paper

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.

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