相关论文: Persistent currents on graphs

Stream graphs model highly dynamic networks in which nodes and/or links arrive and/or leave over time. Strongly connected components in stream graphs were defined recently, but no algorithm was provided to compute them. We present here…

We consider stochastic motion of a particle on a cyclic graph with arbitrarily periodic time dependent kinetic rates. We demonstrate duality relations for statistics of currents in this model and in its continuous version of a diffusion in…

We compute the joint large deviation rate functional in the limit of large time for the current flowing through the edges of a finite graph on which a boundary-driven system of stochastic particles evolves with zero-range dynamics.This…

In this brief tutorial review, I show how phase coherent properties of disordered conductors can be described in a simple and unified way. These properties include transport properties like weak-localization correction and universal…

A p-n junction, induced in graphene by gating, works to contrast the edge states of electrons and holes on each side of it. In a magnetic field those edge states carry two species of persistent current, which are intimately tied to the…

Topological data analysis can provide insight on the structure of weighted graphs and digraphs. However, some properties underlying a given (di)graph are hardly mappable to simplicial complexes. We introduce \textit{steady} and…

We propose a procedure to generate dynamical networks with bursty, possibly repetitive and correlated temporal behaviors. Regarding any weighted directed graph as being composed of the accumulation of paths between its nodes, our…

We consider diffusive lattice gases on a ring and analyze the stability of their density profiles conditionally to a current deviation. Depending on the current, one observes a phase transition between a regime where the density remains…

Power grids are undergoing major changes from a few large producers to smart grids build upon renewable energies. Mathematical models for power grid dynamics have to be adapted to capture, when dynamic nodes can achieve synchronization to a…

Spatial intensity correlations between waves transmitted through random media are analyzed within the framework of the random matrix theory of transport. Assuming that the statistical distribution of transfer matrices is isotropic, we found…

Surface sensitive electric current measurements are important experimental tools poorly corroborated by theoretical models. We show that the drift-diffusion equations offer a framework for a consistent description of such experiments. The…

The effect of point defects on persistent currents in mesoscopic systems is studied in a simple tight-binding model. Using an analogy with the treatment of the critical quantum Ising chain with defects, conformal invariance techniques are…

We present faster algorithms for approximate maximum flow in undirected graphs with good separator structures, such as bounded genus, minor free, and geometric graphs. Given such a graph with $n$ vertices, $m$ edges along with a recursive…

We study the wave transport through a disordered system inside a waveguide. The expectation value of the complex reflection and transmission coefficients (the coherent fields) as well as the transmittance and reflectance are obtained…

Despite the obvious similarities between the metrics used in topological data analysis and those of optimal transport, an optimal-transport based formalism to study persistence diagrams and similar topological descriptors has yet to come.…

Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…

Random graphs are more and more used for modeling real world networks such as evolutionary networks of proteins. For this purpose we look at two different models and analyze how properties like connectedness and degree distributions are…

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

Since its first isolation in 2004, graphene has been found to host a plethora of unusual electronic transport phenomena, making it a fascinating system for fundamental studies in condensed-matter physics as well as offering tremendous…

We analyze how the transient dynamics of large dynamical systems in the vicinity of a stationary point, modeled by a set of randomly coupled linear differential equations, depends on the network topology. We characterize the transient…