Second order perturbation theory for embedded eigenvalues

Jérémy Faupin (1) , Jacob Møller (2) , Erik Skibsted (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 Aarhus University [Aarhus]

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.

Domaines: Physique mathématique [math-ph]

Jérémy Faupin, Jacob Møller, Erik Skibsted. Second order perturbation theory for embedded eigenvalues. Communications in Mathematical Physics, 2011, 306, pp.193-228. ⟨10.1007/s00220-011-1278-x⟩. ⟨hal-01279964⟩