Resolvent Convergence to Dirac Operators on Planar Domains

Jean-Marie Barbaroux, Horia Cornean, Loïc Le Treust, Edgardo Stockmeyer

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2 Citations (Scopus)

Abstract

Consider a Dirac operator defined on the whole plane with a mass term of size m supported outside a domain Ω. We give a simple proof for the norm resolvent convergence, as m goes to infinity, of this operator to a Dirac operator defined on Ω 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.

Original languageEnglish
JournalAnnales Henri Poincare
Volume20
Issue number6
Pages (from-to)1877-1891
Number of pages15
ISSN1424-0637
DOIs
Publication statusPublished - Jun 2019

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