Instability of pre-existing resonances under a small constant electric field

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 $f\to0$. 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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