This paper reviews recent advances in continuous-time quantum walks (CTQW) and their
application to transport in various systems. The introduction gives a brief survey of the …

The development of quantum walks in the context of quantum computation, as
generalisations of random walk techniques, has led rapidly to several new quantum …

We formulate and discuss one-particle quantum scattering theory on an arbitrary finite graph
with n open ends and where we define the Hamiltonian to be (minus) the Laplace operator …

A quantum graph is a graph equipped with a self-adjoint differential or pseudodifferential
Hamiltonian. Such graphs have been studied recently in relation to some problems of …

We quantize graphs (networks) which consist of a finite number of bonds and vertices. We
show that the spectral statistics of fully connected graphs is well reproduced by random …

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 …

In this work, we discuss the resonance states of a quantum particle in a periodic potential
plus a static force. Originally, this problem was formulated for a crystal electron subject to a …

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 …

Abstract Watts and Strogatz [Nature (London) 393, 440 (1998)] have recently introduced a
model for disordered networks and reported that, even for very small values of the disorder p …