Related papers: Dirac Particles in Transparent Quantum Graphs: Tun…
We consider quantum graphs with transparent branching points. To design such networks, the concept of transparent boundary conditions is applied to the derivation of the vertex boundary conditions for the linear Schrodinger equation on…
In this paper, we discuss the concept of quantum graphs with transparent vertices by considering the case where the graph interacts with an external time-independent field. In particular, we address the problem of transparent boundary…
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum…
A multi-branch quantum circuit is considered from the viewpoint of coherent electron or wave transport. Starting with the closed system, we give analytical conditions for the appearance of two isolated localized states out of the energy…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
We systematise and develop a graphical approach to the investigations of quantum integrable vertex statistical models and the corresponding quantum spin chains. The graphical forms of the unitarity and various crossing relations are…
Quantum graphs are commonly used as models of complex quantum systems, for example molecules, networks of wires, and states of condensed matter. We consider quantum statistics for indistinguishable spinless particles on a graph,…
Motivated by the conduction properties of graphene discovered and studied in the last decades, we consider the quantum dynamics of a massless, charged, spin 1/2 relativistic particle in three dimensional space-time, in the presence of an…
This work deals with quantum transport in open quantum graphs. We consider the case of complete graphs on $n$ vertices with an edge removed and attached to two leads, to represent the entrance and exit channels, from where we calculate the…
We suggest a way of confining quasiparticles by an external potential in a small region of a graphene strip. Transversal electron motion plays a crucial role in this confinement. Properties of thus obtained graphene quantum dots are…
The motion of a relativistic particle is linked to its spin by the Dirac equation. Remarkably, electrons in two-dimensional materials can mimic such Dirac particles but must always appear in pairs of opposite spin chirality. Using…
Interest on 2 + 1 dimensional electron systems has increased considerably after the realization of novel properties of graphene sheets, in which the behaviour of electrons is effectively described by relativistic equations. Having this fact…
The aim of the present paper is to analyse the spectrum of Laplace and Dirac type operators on metric graphs. In particular, we show for equilateral graphs how the spectrum (up to exceptional eigenvalues) can be described by a natural…
Classical mechanical treatment of charged particle beam optics is so far very satisfactory from a practical point of view in applications ranging from electron microscopy to accelerator technology. However, it is desirable to understand the…
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 present and analyze two mathematical models for the self consistent quantum transport of electrons in a graphene layer. We treat two situations. First, when the particles can move in all the plane $\RR^2$, the model takes the form of a…
There is evidence for existence of massless Dirac quasi-particles in graphene, which satisfy Dirac equation in (1+2) dimensions near the so called Dirac points which lie at the corners at the graphene's brilluoin zone. We revisit the…
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,…
Quantum teleportation plays a key role in modern quantum technologies. Thus, it is of much interest to generate alternative approaches or representations aimed at allowing us a better understanding of the physics involved in the process…
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…