TY - JOUR
T1 - Two-dimensional Dirac operators with singular interactions supported on closed curves
AU - Behrndt, Jussi
AU - Holzmann, Markus
AU - Ourmieres-Bonafos, Thomas
AU - Pankrashkin, Konstantin
PY - 2020/11/1
Y1 - 2020/11/1
N2 - We study the two-dimensional Dirac operator with a class of interface conditions along a smooth closed curve, which model the so-called electrostatic and Lorentz scalar interactions of constant strengths, and we provide a rigorous description of their self-adjoint realizations and their qualitative spectral properties. We are able to cover in a uniform way all so-called critical combinations of coupling constants, for which there is a loss of regularity in the operator domain. For the case of a non-zero mass term, this results in an additional point in the essential spectrum, which reflects the creation of an infinite number of eigenvalues in the central gap, and the position of this point can be made arbitrary by a suitable choice of the parameters. The analysis is based on a combination of the extension theory of symmetric operators with a detailed study of boundary integral operators viewed as periodic pseudodifferential operators.
AB - We study the two-dimensional Dirac operator with a class of interface conditions along a smooth closed curve, which model the so-called electrostatic and Lorentz scalar interactions of constant strengths, and we provide a rigorous description of their self-adjoint realizations and their qualitative spectral properties. We are able to cover in a uniform way all so-called critical combinations of coupling constants, for which there is a loss of regularity in the operator domain. For the case of a non-zero mass term, this results in an additional point in the essential spectrum, which reflects the creation of an infinite number of eigenvalues in the central gap, and the position of this point can be made arbitrary by a suitable choice of the parameters. The analysis is based on a combination of the extension theory of symmetric operators with a detailed study of boundary integral operators viewed as periodic pseudodifferential operators.
KW - Boundary triple
KW - Dirac operator with singular interaction
KW - Periodic pseudodifferential operators
KW - Self-adjoint extension
UR - http://www.scopus.com/inward/record.url?scp=85087953813&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2020.108700
DO - 10.1016/j.jfa.2020.108700
M3 - Article
SN - 0022-1236
VL - 279
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 8
M1 - 108700
ER -