Relaxation dynamics of the electron distribution in the Coulomb blockade problem

TL;DR

This paper investigates how electron distributions relax over time in a single electron transistor, revealing that Coulomb interactions significantly alter the typical exponential relaxation behavior.

Contribution

It derives a quantum kinetic equation for electron relaxation considering Coulomb interactions without coherence, providing analytical solutions in different blockade regimes.

Findings

Relaxation deviates from exponential decay due to Coulomb effects

Analytical solutions describe electron distribution evolution

Strong Coulomb blockade modifies relaxation dynamics

Abstract

We study the relaxation dynamics of electron distribution function on the island of a single electron transistor. We focus on the 'interaction without coherence regime in which an electron coherence can be neglected but quantum fluctuations of charge are strong due to Coulomb interaction. The quantum kinetic equation governing the evolution of the electron distribution function due to escape of electrons to the reservoirs is derived. Analytical solutions for time-dependence of the electron distribution are obtained in the regimes of weak and strong Coulomb blockade. We find that usual exponential in time relaxation is strongly modified due to the presence of Coulomb interaction.