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

[img]
Preview
PDF
Download (232kB) | Preview

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
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: 10 Mar 2017 09:12
URI: http://sro.sussex.ac.uk/id/eprint/55040

View download statistics for this item

📧 Request an update