Waveguides with non-Hermitian boundary conditions

We study the spectrum of the Laplacian in a straight planar strip subject to the non-Hermitian Robin boundary conditions. We define the Laplacian as an m-sectorial operator using the theory of sectorial forms. We deal with the limit situation of the curved strip with infinitely small width. We prove that in this case the non-selfadjoint Robin Laplacian converges to a one-dimensional effective Hamiltonian in the weak-resolvent sense.