General $\delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation

作者: Vladimir Lotoreichik , Albert Mas , Biagio Cassano , Matěj Tušek

DOI:

关键词:

摘要: In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of interaction is performed by decomposing it into linear combination four elementary interactions: electrostatic, Lorentz scalar, magnetic, and fourth one which can be absorbed using unitary transformations. We address self-adjointness spectral description underlying operator, moreover describe its approximation operators regular potentials.

参考文章(53)
Vitor M. Pereira, A. H. Castro Neto, Strain engineering of graphene's electronic structure. Physical Review Letters. ,vol. 103, pp. 046801- ,(2009) , 10.1103/PHYSREVLETT.103.046801
Sergio Albeverio, Solvable Models in Quantum Mechanics ,(1988)
Barry Simon, Michael Reed, Methods of Modern Mathematical Physics ,(1972)
William Charles Hector McLean, Strongly Elliptic Systems and Boundary Integral Equations ,(2000)
Pavel Exner, Leaky Quantum Graphs: A Review arXiv: Mathematical Physics. ,(2007)
J.F. Brasche, P. Exner, Y.A. Kuperin, P. Seba, Schrödinger-Operators with Singular Interactions Journal of Mathematical Analysis and Applications. ,vol. 184, pp. 112- 139 ,(1994) , 10.1006/JMAA.1994.1188
N Dombey, Seventy years of the Klein paradox Physics Reports. ,vol. 315, pp. 41- 58 ,(1999) , 10.1016/S0370-1573(99)00023-X