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Metastable States When the Fermi Golden Rule Constant Vanishes

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Abstract

Resonances appearing by perturbation of embedded non-degenerate eigenvalues are studied in the case when the Fermi Golden Rule constant vanishes. Under appropriate smoothness properties for the resolvent of the unperturbed Hamiltonian, it is proved that the first order Rayleigh–Schrödinger expansion exists. The corresponding metastable states are constructed using this truncated expansion. We show that their exponential decay law has both the decay rate and the error term of order ɛ 4, where ɛ is the perturbation strength.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Aalborg University, Fr. Bajers Vej 7G, 9220, Aalborg Ø, Denmark

    Horia D. Cornean & Arne Jensen

  2. Institute of Mathematics of the Romanian Academy, Research Unit 1, Calea Grivitei 21, 010702, Bucharest, Romania

    Gheorghe Nenciu

Authors
  1. Horia D. Cornean
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  2. Arne Jensen
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  3. Gheorghe Nenciu
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Correspondence to Arne Jensen.

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Communicated by B. Simon

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Cornean, H.D., Jensen, A. & Nenciu, G. Metastable States When the Fermi Golden Rule Constant Vanishes. Commun. Math. Phys. 334, 1189–1218 (2015). https://doi.org/10.1007/s00220-014-2127-5

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  • DOI: https://doi.org/10.1007/s00220-014-2127-5

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