Related papers: Dirac particles on periodic quantum graphs
We study the spectral statistics of quantum (metric) graphs whose vertices are equipped with preferred orientation vertex conditions. When comparing their spectral statistics to those predicted by suitable random matrix theory ensembles,…
It is well known that, in general, part of the spectrum of a graph can be obtained from the adjacency matrix of its quotient graph given by a regular partition. In this paper, we propose a method to obtain all the spectrum, and also the…
The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting operator. For a family of boundary…
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in…
The Dirac equation is solved for triangular and hexagonal graphene quantum dots for different boundary conditions in the presence of a perpendicular magnetic field. We analyze the influence of the dot size and its geometry on their energy…
We show that the Dirac equation can be rewritten as a relation describing the fundamental symmetry group of special topological manifold corresponding to the Dirac wave field. It leads to unification of the time-space and internal…
A new exactly solvable relativistic periodic potential is obtained by the periodic extension of a well-known transparent scalar potential. It is found that the energy band edges are determined by a transcendental equation which is very…
We consider a quantum dot described by a cylindrically symmetric 2D Dirac equation. The potentials representing the quantum dot are taken to be of different types of potential configuration, scalar, vector and pseudo-scalar to enable us to…
We consider the dynamics on a quantum graph as the limit of the dynamics generated by a one-particle Hamiltonian in R^2 with a potential having a deep strict minimum on the graph, when the width of the well shrinks to zero. For a generic…
Transmission probabilities of Dirac fermions in graphene under linear barrier potential oscillating in time are investigated. Solving Dirac equation we end up with the solutions of the energy spectrum depending on several modes coming from…
We introduce the concept of regular quantum graphs and construct connected quantum graphs with discrete symmetries. The method is based on a decomposition of the quantum propagator in terms of permutation matrices which control the way…
We carry the index theory for manifolds with boundary of B\"ar and Ballmann over to first order differential operators on metric graphs. This approach results in a short proof for the index of such operators. Then the self-adjoint…
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 describes the dynamics of topological signals or cochains,…
During the last years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wave function statistics. In the first part of this review we give a detailed introduction to…
The necessary and sufficient conditions are given for a sequence of complex numbers to be the periodic (or antiperiodic) spectrum of non-self-adjoint Dirac operator.
Finding hidden layers in complex networks is an important and a non-trivial problem in modern science. We explore the framework of quantum graphs to determine whether concealed parts of a multi-layer system exist and if so then what is…
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…
We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…
In this paper, we investigate a five-dimensional Dirac fermion on a quantum graph that consists of a single vertex and $N$ loops. We find that the model possesses a rich structure of boundary conditions for wavefunctions on the quantum…
Quantum graphs have recently been introduced as model systems to study the spectral statistics of linear wave problems with chaotic classical limits. It is proposed here to generalise this approach by considering arbitrary, directed graphs…