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Day February 25, 2011

The effective Hamiltonian for thin layers with non-Hermitian Robin-type boundary conditions

Denis Borisov, David Krejcirik

The Laplacian in an unbounded tubular neighbourhood of a hyperplane with non-Hermitian complex-symmetric Robin-type boundary conditions is investigated in the limit when the width of the neighbourhood diminishes. We show that the Laplacian converges in a norm resolvent sense to a self-adjoint Schroedinger operator in the hyperplane whose potential is expressed solely in terms of the boundary coupling function. As a consequence, we are able to explain some peculiar spectral properties of the non-Hermitian Laplacian by known results for Schroedinger operators.

http://arxiv.org/abs/1102.5051
Spectral Theory (math.SP); Mathematical Physics (math-ph)