During the last few years quantum graphs have become a paradigm of quantum chaos with
applications from spectral statistics to chaotic scattering and wavefunction statistics. In the …

Small-radius tubular structures have attracted considerable attention in the last few years,
and are frequently used in different areas such as Mathematical Physics, Spectral Geometry …

In order to become worldly things, that is, deeds and facts and events and patterns of
thoughts or ideas,[action, speech, and thought] must first be seen, heard, and remembered …

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 define the topological Dirac equation describing the evolution of a topological wave
function on networks or on simplicial complexes. On networks, the topological wave function …

Here we review the many aspects and distinct phenomena associated to quantum dynamics
on general graph structures. For so, we discuss such class of systems under the energy …

Three different inverse problems for the Schrödinger operator on a metric tree are
considered, so far with standard boundary conditions at the vertices. These inverse …

This open access book gives a systematic introduction into the spectral theory of differential
operators on metric graphs. Main focus is on the fundamental relations between the …

The main objective of the present work is to study the negative spectrum of (differential)
Laplace operators on metric graphs as well as their resolvents and associated heat …

We study the case in which the nonlinear Schrödinger equation (NLSE) on simple networks
consisting of vertices and bonds has an infinite number of constants of motion and becomes …