Related papers: Quantum graph as a quantum spectral filter
The control of the quantum transport is an issue of current interest for the construction of new devices. In this work, we investigate this possibility in the realm of quantum graphs. The study allows the identification of two distinct…
Graph kernels are often used in bioinformatics and network applications to measure the similarity between graphs; therefore, they may be used to construct efficient graph classifiers. Many graph kernels have been developed thus far, but to…
We report a method that exploits a connection between quantum contextuality and graph theory to reveal any form of quantum contextuality in high-precision experiments. We use this technique to identify a graph which corresponds to an…
Quantum networks are often modelled using Schroedinger operators on metric graphs. To give meaning to such models one has to know how to interpret the boundary conditions which match the wave functions at the graph vertices. In this article…
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
The graphene membrane irradiated by weak activating alternative electric field in terahertz range was considered. The quantum approach based on the time-dependent density matrix method was used. The exact solution was obtained for graphene…
Graph signal processing analyzes signals supported on the nodes of a graph by defining the shift operator in terms of a matrix, such as the graph adjacency matrix or Laplacian matrix, related to the structure of the graph. With respect to…
We propose that a magnetic quantum wire composed of magnetic and non-magnetic atomic sites can be used as a spin filter for a wide range of applied bias voltage. We adopt a simple tight-binding Hamiltonian to describe the model where the…
{\em Quantum Fourier analysis} is a new subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum…
In the paper we calculate the frequency shift induced on a photon by the interaction with a low density electronic plasma. The technique is the standard perturbation theory of quantum electrodynamics, taking into account the many body…
We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…
We consider a family of quantum graphs $\{(\Gamma,\mathcal{A}_\varepsilon)\}_{\varepsilon>0}$, where $\Gamma$ is a $\mathbb{Z}^n$-periodic metric graph and the periodic Hamiltonian $\mathcal{A}_\varepsilon$ is defined by the operation…
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…
Given an unbalanced open quantum graph, we derive a formula relating sums over its scattering resonances with integrals outside a strip. We deduce lower bounds on the number of resonances (in bounded regions of the complex plane),that are…
We present a method based on graph theory for evaluation of the inelastic propensity rules for molecules exhibiting complete destructive quantum interference in their elastic transmission. The method uses an extended adjacency matrix…
We study the quantum dynamics of Gaussian wave packets on star graphs whose arms feature each a periodic potential and an external time-dependent field. Assuming that the potentials and the field can be manipulated separately for each arm…
Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free…
We clarify the correspondence between the two approaches to quantum graphs: via quantum adjacency matrices and via quantum relations. We show how the choice of a (possibly non-tracial) weight manifests itself on the quantum relation side…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
We study spectral graph convolutional neural networks (GCNNs), where filters are defined as continuous functions of the graph shift operator (GSO) through functional calculus. A spectral GCNN is not tailored to one specific graph and can be…