Related papers: Persistent currents on graphs
We study the inverse problem of determining the conductivity matrix of an electrical network from the prescribed knowledge of the magnitude of the induced current along the edges coupled with the imposed voltage or injected current on the…
We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…
We thoroughly study the persistent current of noninteracting electrons in one, two, and three dimensional thin rings. We find that the results for noninteracting electrons are more relevant for individual mesoscopic rings than hitherto…
In this paper, we study the construction and transformation of two-dimensional persistent graphs. Persistence is a generalization to directed graphs of the undirected notion of rigidity. In the context of moving autonomous agent formations,…
In this paper we consider a scalar parabolic equation on a star graph; the model is quite general but what we have in mind is the description of traffic flows at a crossroad. In particular, we do not necessarily require the continuity of…
We derive maps relating currents and their divergences in non-abelian U(N) noncommutative gauge theory with the corresponding expressions in the ordinary (commutative) description. For the U(1) theory, in the slowly-varying-field…
Using the properties of the transfer matrix of one-dimensional quantum mechanical systems, we derive a technique to exactly compute the persistent current across a hybrid normal-superconducting-mesoscopic ring pierced by a magnetic flux Phi…
The electronic transport in a system of two quantum rings side-coupled to a quantum wire is studied via a single-band tunneling tight-binding Hamiltonian. We derived analytical expressions for the conductance, density of states and the…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
This work presents a framework for studying temporal networks using zigzag persistence, a tool from the field of Topological Data Analysis (TDA). The resulting approach is general and applicable to a wide variety of time-varying graphs. For…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
In this paper we study integer multiplicity rectifiable currents carried by the subgradient (subdifferential) graphs of semi-convex functions on a $n$-dimensional convex domain, and show a weak continuity theorem with respect to pointwise…
The average persistent current <I> of diffusive electrons in the Hartree-Fock approximation is derived in a simple non-diagrammatic picture. The Fourier expansion directly reflects the winding number decomposition of the diffusive motion…
In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…
An expression for the conductance of interacting electrons in the diffusive regime as a function of the ensemble averaged persistent current and the compressibility of the system is presented. This expression involves only ground-state…
We consider the magnetic field induced by the steady or the quasi-steady electric currents that flow along the straight wires, which are equidistantly arranged on the hyperboloid. The spatial distribution of the magnetic field and the force…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
In this paper, we explore the persistent current in thin superconducting wires and accurately examine the effects of the phase slips on that current. The main result of the paper is the formula for persistent current in terms of the…
Perturbing transition rates in a steady nonequilibrium system, e.g. modelled by a Markov jump process, causes a change in the local currents. Their susceptibility is usually expressed via Green-Kubo relations or their nonequilibrium…
We take account of normal currents that emerge when vortices move. Moving Abrikosov vortices in the bulk and Pearl vortices in thin films are considered. Velocity dependent distributions of both normal and persistent currents are studied in…