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Exponential decay in the stark effect

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Abstract

LetH=−Δ+V+Fx 1 withV(x 1,x ⊥) analytic in the first variable andV(x 1+ia, x ⊥) bounded and decreasing to zero asx → ∞ for eacha ∈ ℝ. Let ψ be an eigenvector of −Δ+V with negative eigenvalue. Among our results we show that forF≠0, (ψ,e −Hψ) decays exponentially at a rate governed by the positions of the resonances ofH. This exponential decay is in marked contrast to “conventional” atomic resonances for which power law decay is the rule.

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Authors and Affiliations

  1. Department of Mathematics, University of Virginia, 22903, Charlottesville, VA, USA

    Ira W. Herbst

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  1. Ira W. Herbst
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Communicated by B. Simon

Research supported by NSF Grant No. MCS 78-00101.

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Herbst, I.W. Exponential decay in the stark effect. Commun.Math. Phys. 75, 197–205 (1980). https://doi.org/10.1007/BF01212708

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  • DOI: https://doi.org/10.1007/BF01212708

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