Related papers: On topological states and secular equations for qu…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
We introduce a new model for investigating spectral properties of quantum graphs, a quantum circulant graph. Circulant graphs are the Cayley graphs of cyclic groups. Quantum circulant graphs with standard vertex conditions maintain…
We investigate quantum graphs with infinitely many vertices and edges without the common restriction on the geometry of the underlying metric graph that there is a positive lower bound on the lengths of its edges. Our central result is a…
We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…
We determine the optimum topology of quasi-one dimensional nonlinear optical structures using generalized quantum graph models. Quantum graphs are relational graphs endowed with a metric and a multiparticle Hamiltonian acting on the edges,…
We study topological bound states in quantum dots defined by an electric field in bilayer graphene. An external field is perpendicular to the bilayer and changes sign in a finite region that defines the quantum dot. The electric field opens…
We undertake a study of the notion of a quantum graph over arbitrary finite-dimensional $C^*$-algebras $B$ equipped with arbitrary faithful states. Quantum graphs are realised principally as either certain operators on $L^2(B)$, the quantum…
Boundary conditions in quantum graph vertices are generally given in terms of a unitary matrix $U$. Observing that if $U$ has at most two eigenvalues, then the scattering matrix $\mathcal{S}(k)$ of the vertex is a linear combination of the…
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In…
Quantum graphs are defined by having a Laplacian defined on the edges of a metric graph with boundary conditions on each vertex such that the resulting operator, $\mathbf{L}$, is self-adjoint. We use Neumann boundary conditions although we…
Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of…
In this work, we present a theory for topological phases for quantum systems on tree graphs. Conventionally, topological phases of matter have been studied in regular lattices, but also in quasicrystals and amorphous settings. We consider…
In geometric analysis, an index theorem relates the difference of the numbers of solutions of two differential equations to the topological structure of the manifold or bundle concerned, sometimes using the heat kernels of two higher-order…
We introduce n-particle quantum graphs with singular two-particle interactions in such a way that eigenfunctions can be given in the form of a Bethe ansatz. We show that this leads to a secular equation characterising eigenvalues of the…
Topological phases, edge states, and flat bands in synthetic quantum systems are a key resource for topological quantum computing and noise-resilient information processing. We introduce a scheme based on step-dependent quantum walks on…
The paper is concerned with the number of open gaps in spectra of periodic quantum graphs. The well-known conjecture by Bethe and Sommerfeld (1933) says that the number of open spectral gaps for a system periodic in more than one direction…
We consider a collection of bosonic modes corresponding to the vertices of a graph $\Gamma.$ Quantum tunneling can occur only along the edges of $\Gamma$ and a local self-interaction term is present. Quantum entanglement of one vertex with…
In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin…
Quantum entanglement and classical topology are two distinct phenomena that are difficult to be connected together. Here we discover that an open bosonic quadratic chain exhibits topology-induced entanglement effect. When the system is in…
In 2019, Aterias et al. constructed pairs of quantum isomorphic, non-isomorphic graphs from linear constraint systems. This article deals with quantum automorphisms and quantum isomorphisms of colored versions of those graphs. We show that…