# Quantum currents and pair correlation of electrons in a chain of localized dots

## TL;DR

This paper analyzes quantum electron transport in a chain of localized dots, deriving an equivalent circuit model, exact current solutions, and correlation functions to understand the effects of interactions, dissipation, and virtual currents.

## Contribution

It provides an exact solution for quantum currents and a detailed analysis of pair correlations in a chain of localized dots, including an analytical RPA response function.

## Key findings

- Derived an equivalent RCL circuit model for quantum transport.
- Obtained exact solutions for electric-field induced currents.
- Calculated the pair correlation function including structure factors.

## Abstract

The quantum transport of electrons in a wire of localized dots by hopping, interaction and dissipation is calculated and a representation by an equivalent RCL circuit is found. The exact solution for the electric-field induced currents allows to discuss the role of virtual currents to decay initial correlations and Bloch oscillations. The dynamical response function in random phase approximation (RPA) is calculated analytically with the help of which the static structure function and pair correlation function are determined. The pair correlation function contains a form factor from the Brillouin zone and a structure factor caused by the localized dots in the wire.