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Resolvent convergence to Dirac operators on planar domains. (English) Zbl 1414.81103
Summary: 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.

##### MSC:
 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 46N50 Applications of functional analysis in quantum physics 81Q37 Quantum dots, waveguides, ratchets, etc. 34L10 Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators 47A10 Spectrum, resolvent
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