Charge and currents distribution in graphs

TL;DR

This paper investigates charge and current distributions in wire networks modeled as graphs connected to leads, analyzing their correlations and scattering properties in out-of-equilibrium conditions.

Contribution

It introduces a detailed analysis of charge and current distributions in quantum graphs with scalar potentials, focusing on scattering and weak connectivity effects.

Findings

Charge correlations depend on the scattering matrix.

Current distribution varies with graph connectivity and potential.

Weak coupling to leads influences charge and current behavior.

Abstract

We consider graphs made of one-dimensional wires connected at vertices, and on which may live a scalar potential. We are interested in a scattering situation where such a network is connected to infinite leads. We study the correlations of the charge in such graphs out of equilibrium, as well as the distribution of the currents in the wires, inside the graph. These quantities are related to the scattering matrix of the graph. We discuss the case where the graph is weakly connected to the wires.