Semiclassical Szego limit of resonance clusters for the hydrogen atom Stark Hamiltonian

Details Semiclassical Szego limit of resonance clusters for the hydrogen atom Stark Hamiltonian Semiclassical Szego limit of resonance clusters for the hydrogen atom Stark Hamiltonian

2011-04-22

arxiv.org/abs/1104.4466v1

Physics

Mathematical Physics

Scientific paper

We study the weighted averages of resonance clusters for the hydrogen atom with a Stark electric field in the weak field limit. We prove a semiclassical Szego-type theorem for resonance clusters showing that the limiting distribution of the resonance shifts concentrates on the classical energy surface corresponding to a rescaled eigenvalue of the hydrogen atom Hamiltonian. This result extends Szego-type results on eigenvalue clusters to resonance clusters. There are two new features in this work: first, the study of resonance clusters requires the use of non self-adjoint operators, and second, the Stark perturbation is unbounded so control of the perturbation is achieved using localization properties of coherent states corresponding to hydrogen atom eigenvalues.

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