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On Rayleigh Scattering in Non-Relativistic Quantum Electrodynamics

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Abstract

We consider a particle system coupled to the quantized electromagnetic or phonon field. Assuming that the coupling is small enough and that Fermi’s Golden Rule is satisfied, we prove asymptotic completeness for Rayleigh scattering on the states for which the expectation of either the photon/phonon number operator or an operator testing the photon/phonon infrared behaviour is uniformly bounded on corresponding dense sets. By extending a recent result of De Roeck and Kupiainen in a straightforward way, we show that the second of these conditions is satisfied for the spin-boson model.

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Authors and Affiliations

  1. Institut Elie Cartan de Lorraine, Université de Lorraine, Ile du Saulcy, 57045, Metz Cedex 1, France

    Jérémy Faupin

  2. Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4, Canada

    Israel Michael Sigal

Authors
  1. Jérémy Faupin
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  2. Israel Michael Sigal
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Correspondence to Israel Michael Sigal.

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Communicated by H. Spohn

To Jürg Fröhlich whose vision and ideas shaped the non-relativistic quantum electrodynamics

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Faupin, J., Sigal, I.M. On Rayleigh Scattering in Non-Relativistic Quantum Electrodynamics. Commun. Math. Phys. 328, 1199–1254 (2014). https://doi.org/10.1007/s00220-014-1883-6

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