Annales Henri Poincaré

, Volume 16, Issue 12, pp 2783–2835 | Cite as

Instability of Pre-Existing Resonances Under a Small Constant Electric Field

  • Ira Herbst
  • Juliane RamaEmail author


Two simple model operators are considered which have pre-existing resonances. A potential corresponding to a small electric field, f, is then introduced and the resonances of the resulting operator are considered as f → 0. It is shown that these resonances are not continuous in this limit. It is conjectured that a similar behavior will appear in more complicated models of atoms and molecules. Numerical results are presented.


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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of VirginiaCharlottesvilleUSA
  2. 2.Institut für MathematikUniversität PotsdamPotsdamGermany

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