Essential self-adjointness of symmetric first-order differential systems and confinement of Dirac particles on bounded domains in $\mathbb{R}^d$
| Autor: | Irina Nenciu, Gheorghe Nenciu, Ryan Obermeyer |
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| Rok vydání: | 2020 |
| Předmět: |
Dirac (software)
Scalar (mathematics) Boundary (topology) FOS: Physical sciences Dirac operator 01 natural sciences Omega symbols.namesake Mathematics - Analysis of PDEs Operator (computer programming) 0103 physical sciences FOS: Mathematics 0101 mathematics Mathematical Physics Lorentz scalar Mathematical physics Physics 010102 general mathematics Statistical and Nonlinear Physics Mathematical Physics (math-ph) 16. Peace & justice Functional Analysis (math.FA) Mathematics - Functional Analysis Bounded function symbols 010307 mathematical physics Analysis of PDEs (math.AP) |
| DOI: | 10.48550/arxiv.2010.09816 |
| Popis: | We prove essential self-adjointness of Dirac operators with Lorentz scalar potentials which grow sufficiently fast near the boundary $\partial\Omega$ of the spatial domain $\Omega\subset\mathbb R^d$. On the way, we first consider general symmetric first order differential systems, for which we identify a new, large class of potentials, called scalar potentials, ensuring essential self-adjointness. Furthermore, using the supersymmetric structure of the Dirac operator in the two dimensional case, we prove confinement of Dirac particles, i.e. essential self-adjointness of the operator, solely by magnetic fields $\mathcal{B}$ assumed to grow, near $\partial\Omega$, faster than $1/\big(2\text{dist} (x, \partial\Omega)^2\big)$. Comment: 40 pages, minor typos corrected and a new Comment 5 added to Section 7 |
| Databáze: | OpenAIRE |
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