Instability of Resonances Under Stark Perturbations

Arne Jensen, Kenji Yajima

Research output: Contribution to journalJournal articleResearchpeer-review


Let Hε=-d2dx2+εx+V, ε≥ 0 , on L 2(R). Let V=∑k=1Nck|ψk⟩⟨ψk| be a rank N operator, where the ψ k∈ L 2(R) are real, compactly supported, and even. Resonances are defined using analytic scattering theory. The main result is that if ζ n, Imζn<0, are resonances of Hεn for a sequence ε n↓ 0 as n→ ∞ and ζ n→ ζ as n→ ∞, Imζ0<0, then ζ is not a resonance of H.

Original languageEnglish
JournalAnnales Henri Poincare
Issue number2
Pages (from-to)675-687
Number of pages13
Publication statusPublished - 5 Feb 2019


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