Kungsman, J and Melgaard, M (2014) Existence of Dirac resonances in the semi-classical limit. Dynamics of Partial Differential Equations, 11 (4). pp. 381-395. ISSN 1548-159X
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Abstract
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⟩−δ at infinity for some δ>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 supV+1 and infV−1. We also provide a lower bound for the number of resonances near these points expressed in terms of the semiclassical parameter.
Item Type: | Article |
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Keywords: | Resonance, Dirac operator, Trace formulas |
Schools and Departments: | School of Mathematical and Physical Sciences > Mathematics |
Subjects: | Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems |
Depositing User: | Michael Melgaard |
Date Deposited: | 30 Jun 2015 08:23 |
Last Modified: | 03 Feb 2020 13:34 |
URI: | http://sro.sussex.ac.uk/id/eprint/55040 |
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