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

Abstract

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.

9 pages

References in corpus (4)

• On a waveguide with frequently alternating boundary conditions: homogenized Neumann condition
• Perfect transmission scattering as a PT-symmetric spectral problem
• Effective Hamiltonians for Thin Dirichlet Tubes with Varying Cross-Section
• Non-Hermitian spectral effects in a PT-symmetric waveguide