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

2024/03/25 by Duran, Joaquim, Mas, Albert · 2 citations
#35P05 #35Q40 (Primary) #47A10 #81Q10 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2403.17057

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.

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• Congruence of Dirac operators with applications to generalized MIT bag models
• A connection between quantum dot Dirac operators and ∂-Robin Laplacians in the context of shape optimization problems

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