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We consider a pair of parallel straight quantum waveguides coupled laterally through a window of a width ℓ in the common boundary. We show that such a system has at least one bound state for any ℓ > 0. We find the corresponding eigenvalues and eigenfunctions numerically using the mode–matching method, and discuss their behavior in several situations. We(More)
We study spectral properties of Dirichlet Laplacian on the conical layer of the opening angle π − 2θ and thickness equal to π. We demonstrate that below the continuum threshold which is equal to one there is an infinite sequence of isolated eigenvalues and analyze properties of these geometrically induced bound states. By numerical computation we find(More)
Recently, PT symmetry of many single-particle non-Hermitian Hamiltonians has been conjectured sufficient for keeping their spectrum real. We show that and how the similar concept of a “weakened Hermiticity” can be extended to some exactly solvable twoand three-particle models. PACS 03.65.Ge, 03.65.Fd February 1, 2008, ptcal.tex file 1 e-mail:(More)
We analyze two-dimensional Schrödinger operators with the potential |xy| − λ(x + y) where p ≥ 1 and λ ≥ 0, which exhibit an abrupt change of its spectral properties at a critical value of the coupling constant λ. We show that in the supercritical case the spectrum covers the whole real axis. In contrast, for λ below the critical value the spectrum is purely(More)
Motivated by a recent application of quantum graphs to model the anomalous Hall effect we discuss quantum graphs the vertices of which exhibit a preferred orientation. We describe an example of such a vertex coupling and analyze the corresponding band spectra of lattices with square and hexagonal elementary cells showing that they depend heavily on the(More)