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Existence of Dirac resonances in the semi-classical limit

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posted on 2023-06-08, 21:19 authored by J Kungsman, Michael MelgaardMichael Melgaard
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?-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 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.

History

Publication status

  • Published

File Version

  • Published version

Journal

Dynamics of Partial Differential Equations

ISSN

1548-159X

Publisher

International Press

Issue

4

Volume

11

Page range

381-395

Department affiliated with

  • Mathematics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2015-06-30

First Open Access (FOA) Date

2019-08-13

First Compliant Deposit (FCD) Date

2019-08-13

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