Counting Statistics in Multi-stable Systems

TL;DR

This paper derives generic properties of full counting statistics in multi-stable quantum transport systems, revealing how initial conditions and system parameters influence distribution shapes and cumulant divergence, with implications for probing background charges.

Contribution

It introduces a microscopic model for stochastic transport in multi-stable systems and analyzes the temporal evolution and asymptotics of counting statistics, highlighting new insights into system behavior.

Findings

Counting statistics transition from multi-modal to broad uni-modal distributions.

Long-term asymptotics show divergence of cumulants in large transport systems.

Single resonant level statistics can probe background charge configurations.

Abstract

Using a microscopic model for stochastic transport through a single quantum dot that is modified by the Coulomb interaction of environmental (weakly coupled) quantum dots, we derive generic properties of the full counting statistics for multi-stable Markovian transport systems. We study the temporal crossover from multi-modal to broad uni-modal distributions depending on the initial mixture, the long-term asymptotics and the divergence of the cumulants in the limit of a large number of transport branches. Our findings demonstrate that the counting statistics of a single resonant level may be used to probe background charge configurations.