Active Brownian Motion in Threshold Distribution of a Coulomb Blockade Model

TL;DR

This paper analytically derives the threshold voltage distribution in Coulomb blockade arrays, revealing its relation to active Brownian motion and comparing it with classical stochastic processes, providing insights into nonlinear conductance behavior.

Contribution

It introduces an analytical derivation of the threshold voltage distribution for Coulomb blockade arrays and links it to active Brownian motion, expanding understanding of nonlinear conductance.

Findings

Distribution satisfies a novel Fokker-Planck equation

Distribution is equivalent to the number of upward steps in aligned objects

Comparison with Wigner and Ornstein-Uhlenbeck processes

Abstract

Randomly-distributed offset charges affect the nonlinear current-voltage property via the fluctuation of the threshold voltage of Coulomb blockade arrays. We analytically derive the distribution of the threshold voltage for a model of one-dimensional locally-coupled Coulomb blockade arrays, and propose a general relationship between conductance and the distribution. In addition, we show the distribution for a long array is equivalent to the distribution of the number of upward steps for aligned objects of different height. The distribution satisfies a novel Fokker-Planck equation corresponding to active Brownian motion. The feature of the distribution is clarified by comparing it with the Wigner and Ornstein-Uhlenbeck processes. It is not restricted to the Coulomb blockade model, but instructive in statistical physics generally.