# Existence of Dirac resonances in the semi-classical limit

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 $\langle x \rangle ^{-\d }$ at infinity for some $\d >0$. 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.

Item Type: Article resonance, Dirac operator, trace formulas School of Mathematical and Physical Sciences > Mathematics Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems Michael Melgaard 30 Jun 2015 08:23 10 Mar 2017 09:12 http://srodev.sussex.ac.uk/id/eprint/55040

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