On the spectral properties of Dirac operators with electrostatic delta-shell interactions

0488733 - ÚJF 2019 RIV NL eng J - Journal Article
Behrndt, J. - Exner, Pavel - Holzmann, M. - Lotoreichik, Vladimir
On the spectral properties of Dirac operators with electrostatic delta-shell interactions.
Journal de Mathematiques Pures et Appliquees. Roč. 111, č. 3 (2018), s. 47-78. ISSN 0021-7824. E-ISSN 1776-3371
R&D Projects: GA ČR(CZ) GA14-06818S
Institutional support: RVO:61389005
Keywords : Dirac operator * self-adjoint extension * shell interaction * spectral properties
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 1.961, year: 2018

In this paper the spectral properties of Dirac operators A(eta), with electrostatic delta-shell interactions of constant strength eta supported on compact smooth surfaces in R-3 are studied. Making use of boundary triple techniques a Krein type resolvent formula and a Birman Schwinger principle are obtained. With the help of these tools some spectral, scattering, and asymptotic properties of An are investigated. In particular, it turns out that the discrete spectrum of A(eta), inside the gap of the essential spectrum is finite, the difference of the third powers of the resolvents of A(eta), and the free Dirac operator A(0) is trace class, and in the nonrelativistic limit A(eta), converges in the norm resolvent sense to a Schrodinger operator with an electric delta-potential of strength eta.
Permanent Link: http://hdl.handle.net/11104/0283275