Resolvent convergence to Dirac operators on planar domains
Mathematical Physics
2019-06-26 v1 math.MP
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.
Keywords
Cite
@article{arxiv.1810.02957,
title = {Resolvent convergence to Dirac operators on planar domains},
author = {Jean-Marie Barbaroux and Horia D. Cornean and Loïc Le Treust and Edgardo Stockmeyer},
journal= {arXiv preprint arXiv:1810.02957},
year = {2019}
}