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Second order perturbation theory for embedded eigenvalues

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  • Department of Mathematical Sciences
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.
Original languageEnglish
JournalCommunications in Mathematical Physics
Pages (from-to)193-228
Number of pages36
Publication statusPublished - 2011

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