Flat energy bands of model lattice Hamiltonians provide a key ingredient in designing
dispersionless wave excitations and have become a versatile platform to study various …

The Hatano-Nelson and the non-Hermitian Su-Schrieffer-Heeger models are paradigmatic
examples of non-Hermitian systems that host nontrivial boundary phenomena. In this work …

We explore the scattering of waves in designed asymmetric one-dimensional waveguide
networks. We show that the reflection between two ports of an asymmetric network can be …

Latent symmetries are hidden symmetries which become manifest by performing a reduction
of a given discrete system into an effective lower-dimensional one. We show how latent …

Graph Spectra and Continuous Quantum Walks Gabriel Coutinho, Chris Godsil Page 1 Graph
Spectra and Continuous Quantum Walks Gabriel Coutinho, Chris Godsil January 1, 2021 Page …

Degeneracies in the energy spectra of physical systems are commonly considered to be
either of accidental character or induced by symmetries of the Hamiltonian. We develop an …

We study perfect state transfer in Kendon's model of discrete quantum walks. In particular,
we give a characterization of perfect state transfer purely in terms of the graph spectra, and …

We establish the theory for pretty good state transfer in discrete-time quantum walks. For a
class of walks, we show that pretty good state transfer is characterized by the spectrum of …

We explore algebraic and spectral properties of weighted graphs containing twin vertices
that are useful in quantum state transfer. We extend the notion of adjacency strong …

Two emerging topics in graph theory are the study of cospectral vertices of a graph, and the
study of isospectral reductions of graphs. In this paper, we prove a fundamental relationship …