Abstract
The resolvent of the operatorH 0(ε, θ)=−Δe -20+εx 1 e θ is not analytic in θ for θ in a neighborhood of a real point, if the electric field ε is non-zero. (One manifestation of this singular behavior is that for 0<|Im θ|<π/3,H 0(ε, θ) has no spectrum in the finite plane.) Nevertheless it is shown that the techniques of dilation analyticity still can be used to discuss the long-lived states (resonances) of a system described by a Hamiltonian of the formH=−Δ+εx 1+V(x).
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Communicated by J. Ginibre
Research supported by NSF Grant No. MCS 78-00101
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Herbst, I.W. Dilation analyticity in constant electric field. Commun.Math. Phys. 64, 279–298 (1979). https://doi.org/10.1007/BF01221735
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DOI: https://doi.org/10.1007/BF01221735