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Existence of Dirac resonances in the semi-classical limit
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2014 (English)In: Dynamics of Partial Differential Equations, ISSN 1548-159X, Vol. 11, no 4, 381-395 p.Article in journal (Refereed) Published
Abstract [en]

We study the existence of quantum resonances of the three-dimensional semiclassical Dirac operator perturbed by smooth, bounded and real-valued scalar potentials V decaying like < x >(-delta) at infinity for some delta > 0. By studying analytic singularities of a certain distribution related to V and by combining two trace formulas, we prove that the perturbed Dirac operators possess resonances near sup V + 1 and inf V - 1. We also provide a lower bound for the number of resonances near these points expressed in terms of the semiclassical parameter.

Place, publisher, year, edition, pages
2014. Vol. 11, no 4, 381-395 p.
National Category
Mathematical Analysis
Research subject
URN: urn:nbn:se:uu:diva-223459ISI: 000348668600005OAI: oai:DiVA.org:uu-223459DiVA: diva2:713099
Available from: 2014-04-20 Created: 2014-04-20 Last updated: 2015-03-05Bibliographically approved

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