Resonances for the radial Dirac operators

Article type: Research Article

Authors: Iantchenko, Alexei^{a; *} | Korotyaev, Evgeny^b

Affiliations: [a] Malmö högskola, Teknik och samhälle, Malmö, Sweden. E-mail: [email protected] | [b] Mathematical Physics Department, Faculty of Physics, St. Petersburg State University, St. Petersburg, Russia. E-mail: [email protected]

Correspondence: [*] Corresponding author: Alexei Iantchenko, Malmö högskola, Teknik och samhälle, 205 06 Malmö, Sweden. E-mail: [email protected].

Abstract: We consider the radial Dirac operator with compactly supported potentials. We study resonances as the poles of scattering matrix or equivalently as the zeros of modified Fredholm determinant. We obtain the following properties of the resonances: (1) asymptotics of counting function, (2) in the massless case we get the trace formula in terms of resonances.

Keywords: resonances, 1D Dirac

DOI: 10.3233/ASY-151298

Journal: Asymptotic Analysis, vol. 93, no. 4, pp. 327-370, 2015