Calculus of Variations and Geometric Measure Theory

J. Duran Lamiel - A. Mas

Convergence of generalized MIT bag models to Dirac operators with zigzag boundary conditions

created by duranlamiel on 17 Oct 2024

[BibTeX]

Published Paper

Inserted: 17 oct 2024
Last Updated: 17 oct 2024

Journal: Analysis and Mathematical Physics
Volume: 14
Number: 85
Pages: 23
Year: 2024
Doi: https://doi.org/10.1007/s13324-024-00946-7

ArXiv: 2403.17057 PDF

Abstract:

This work addresses the resolvent convergence of generalized MIT bag operators to Dirac operators with zigzag type boundary conditions. We prove that the convergence holds in strong but not in norm resolvent sense. Moreover, we show that the only obstruction for having norm resolvent convergence is the existence of an eigenvalue of infinite multiplicity for the limiting operator. More precisely, we prove the convergence of the resolvents in operator norm once projected into the orthogonal of the corresponding eigenspace.