Statistics of energy dissipation in a quantum dot operating in the cotunneling regime

TL;DR

This paper analyzes the energy dissipation statistics in a quantum dot during inelastic cotunneling, deriving analytical expressions for the distribution and moments, revealing divergence behavior and deviations from fluctuation relations.

Contribution

We analytically derive the cumulant generating function and explore the energy dissipation PDF in quantum dots under cotunneling, highlighting unique divergence and fluctuation properties.

Findings

Fano factor diverges as T^3/(eV)^2 at low bias

Fano factor approaches 3 eV / 5 at high bias

PDF does not satisfy Crooks fluctuation relation

Abstract

At Coulomb blockade valleys inelastic cotunneling processes generate particle-hole excitations in quantum dots (QDs), and lead to energy dissipation. We have analyzed the probability distribution function (PDF) of energy dissipated in a QD due to such processes during a given time interval. We obtained analytically the cumulant generating function, and extracted the average, variance and Fano factor. The latter diverges as $T^3/(eV)^2$ at bias $eV$ smaller than the temperature $T$, and reaches the value $3 eV / 5$ in the opposite limit. The PDF is further studied numerically. As expected, Crooks fluctuation relation is not fulfilled by the PDF. Our results can be verified experimentally utilizing transport measurements of charge.