DPDE-2014-0011-0004-a005.pdf (226.9 kB)
Existence of Dirac resonances in the semi-classical limit
journal contribution
posted on 2023-06-08, 21:19 authored by J Kungsman, Michael MelgaardMichael MelgaardWe 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 EquationsISSN
1548-159XPublisher
International PressExternal DOI
Issue
4Volume
11Page range
381-395Department affiliated with
- Mathematics Publications
Full text available
- Yes
Peer reviewed?
- Yes