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Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field

Abstract:

We consider systems of static nuclei and electrons – atoms and molecules – coupled to the quantized radiation field. The interactions between electrons and the soft modes of the quantized electromagnetic field are described by minimal coupling, ppe A (x), where A(x) is the electromagnetic vector potential with an ultraviolet cutoff. If the interactions between the electrons and the quantized radiation field are turned off, the atom or molecule is assumed to have at least one bound state. We prove that, for sufficiently small values of the fine structure constant α, the interacting system has a ground state corresponding to the bottom of its energy spectrum. For an atom, we prove that its excited states above the ground state turn into metastable states whose life-times we estimate. Furthermore the energy spectrum is absolutely continuous, except, perhaps, in a small interval above the ground state energy and around the threshold energies of the atom or molecule.

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Received: 3 September 1998 / Accepted: 17 March 1999

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Bach, V., Fröhlich, J. & Sigal, I. Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field. Comm Math Phys 207, 249–290 (1999). https://doi.org/10.1007/s002200050726

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  • DOI: https://doi.org/10.1007/s002200050726

Keywords

  • Radiation
  • Excited State
  • Spectral Analysis
  • Energy Spectrum
  • Fine Structure