Dirichlet Laplacian on curved tubes of a constant cross section in two and three dimensions
is investigated. It is shown that if the tube is non-straight and its curvature vanishes …

Trapped modes, localized oscillations in unbounded media, are referred to in different
contexts by various names; acoustic resonances, Rayleigh–Bloch waves, edge waves, array …

The analysis of eigenvalues of Laplace and Schrödinger operators is an important and
classical topic in mathematical physics with many applications. This book presents a …

We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in
bounded Euclidean domains with Dirichlet, Neumann, or Robin boundary condition. We …

This monograph explains the theory of quantum waveguides, that is, dynamics of quantum
particles confined to regions in the form of tubes, layers, networks, etc. The focus is on …

A brief survey on graph models for wave propagation in thin structures is presented. Such
models arise in many areas of mathematics, physics, chemistry and engineering (dynamical …

The wave equation subject to Dirichlet boundary conditions has a bound state in an infinite
tube of constant cross section in any number of dimensions, provided that the tube is not …

The purpose of this text is to set up a few basic notions concerning quantum graphs, to
indicate some areas addressed in the quantum graph research, and to provide some …

We consider a family of compact manifolds which shrinks with respect to an appropriate
parameter to a graph. The main result is that the spectrum of the Laplace–Beltrami operator …

We study the eigenvalue spectrum of Dirichlet Laplacians which model quantum
waveguides associated with tubular regions outside of a bounded domain. Intuitively, our …