Session S30 - Mathematical Methods in Quantum Mechanics

Thursday, July 15, 16:00 ~ 16:25 UTC-3

Resonances for rank one perturbations of Hamiltonians with embedded eigenvalues

Claudio Fernandez

Pontificia Universidad Católica de Chile, Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

We discuss resonances generated by rank one perturbations of selfadjoint operators with eigenvalues embedded in the continuous spectrum. Instability of these eigenvalues is analyzed and almost exponential decay for the associated resonant states is exhibited. We show how these results can be applied to Sturm-Liouville operators. Main tools are the Aronszajn-Donoghue theory for rank one perturbations, a reduction process of the resolvent based on Feshbach-Livsic formula, the Fermi golden rule and a careful analysis of the Fourier transform of quasi-Lorentzian functions. We also show a connection with sojourn time estimates and the spectral concentration phenomenon.

These results are part of a joint work with Bourget, Cortes, Astaburuaga (PUC, Chile) and Del Rio (UNAM, Mexico).

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