Abstract
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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Communicated by Jan Dereziński.
J.R. was supported by the Deutsche Forschungsgemeinschaft (DFG), research grants RA 2020/1-1 and RA 2020/1-2 (and also grant RA 2020/3-1).
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Herbst, I., Rama, J. Instability of Pre-Existing Resonances Under a Small Constant Electric Field. Ann. Henri Poincaré 16, 2783–2835 (2015). https://doi.org/10.1007/s00023-014-0389-2
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DOI: https://doi.org/10.1007/s00023-014-0389-2