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• W2121943734 abstract "Let H be a Schrodinger operator on a Hilbert space H, such that zero is a nondegenerate threshold eigenvalue of H with eigenfunction Ψ0. Let W be a bounded selfadjoint operator satisfying 〈Ψ0,WΨ0〉 > 0. Assume that the resolvent (H − z)−1 has an asymptotic expansion around z = 0 of the form typical for Schrodinger operators on odd-dimensional spaces. Let H(e) = H +eW for e > 0 and small. We show under some additional assumptions that the eigenvalue at zero becomes a resonance for H(e), in the time-dependent sense introduced by A. Orth. No analytic continuation is needed. We show that the imaginary part of the resonance has a dependence on e of the form e2+(ν/2) with the integer ν ≥ −1 and odd. This shows how the Fermi Golden Rule has to be modified in the case of perturbation of a threshold eigenvalue. We give a number of explicit examples, where we compute the location of the resonance to leading order in e." @default.
• W2121943734 created "2016-06-24" @default.
• W2121943734 creator A5085025029 @default.
• W2121943734 creator A5087456588 @default.
• W2121943734 date "2004-01-01" @default.
• W2121943734 modified "2023-09-27" @default.
• W2121943734 title "The Fermi Golden Rule at thresholds" @default.
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