Self-adjoint Extensions of the Two-valley Dirac Operator with Discontinuous Infinite Mass Boundary Conditions

0534046 - ÚJF 2021 RIV HR eng J - Journal Article
Cassano, B. - Lotoreichik, Vladimir
Self-adjoint Extensions of the Two-valley Dirac Operator with Discontinuous Infinite Mass Boundary Conditions.
Operators and Matrices. Roč. 14, č. 3 (2020), s. 667-678. ISSN 1846-3886. E-ISSN 1846-3886
R&D Projects: GA ČR GA17-01706S
Institutional support: RVO:61389005
Keywords : Dirac operator * infinite mass boundary condition * wedge * self-adjoint extensions * mixing the valleys
OECD category: Pure mathematics
Impact factor: 0.624, year: 2020
Method of publishing: Limited access
https://doi.org/10.7153/oam-2020-14-42

We consider the four-component two-valley Dirac operator on a wedge in R-2 with infinite mass boundary conditions, which enjoy a flip at the vertex. We show that it has deficiency indices (1,1) and we parametrize all its self-adjoint extensions, relying on the fact that the underlying two-component Dirac operator is symmetric with deficiency indices (0,1). The respective defect element is computed explicitly. We observe that there exists no self-adjoint extension, which can be decomposed into an orthogonal sum of two two-component operators. In physics, this effect is called mixing the valleys.
Permanent Link: http://hdl.handle.net/11104/0312257