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

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

2011-02-24

arxiv.org/abs/1102.5051v1

Asympt. Anal. 76 (2012), 49-59

Mathematics

Spectral Theory

9 pages

Scientific paper

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.

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