Resolvent convergence to Dirac operators on planar domains

Abstract

Consider a Dirac operator defined on the whole plane with a mass term of size m supported outside a domain Omega. We give a simple proof for the norm resolvent convergence, as m goes to infinity, of this operator to a Dirac operator defined on Omega with infinite mass boundary conditions. The result is valid for bounded and unbounded domains and gives estimates on the speed of convergence. Moreover, the method easily extends when adding external matrix-valued potentials.

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• Spectral optimisation of Dirac rectangles
• Eigenvalue curves for generalized MIT bag models
• Spectral inequality for Dirac right triangles
• Essential self-adjointness of symmetric first-order differential systems and confinement of Dirac particles on bounded domains in ${\mathbb{R}}^d$
• A Poincaré-Steklov map for the MIT bag model