Instantaneous Emission Rate of Electron Transport through a quantum point contact

TL;DR

This paper develops a theoretical framework using the conditional intensity function to describe the time-dependent electron emission rate in quantum point contacts, revealing transitions from Poisson to non-renewal processes as conductance varies.

Contribution

It introduces a novel application of the conditional intensity function to model the history-dependent emission rate in quantum-coherent conductors.

Findings

Emission process transitions from Poisson to non-renewal at full transmission

Conditional intensity function effectively describes emission dynamics

Method provides intuitive understanding of electron emission in quantum conductors

Abstract

We present a theory to describe the instantaneous emission rate of electron transport in quantum-coherent conductors. Due to the Pauli exclusion principle, electron emission events are usually correlated. This makes the emission rate is not a constant, but depends on the history of the emission process. To incorporate such history dependence, in this paper we characterize the emission rate via the conditional intensity function, which has been introduced in the theory of random point process. The conditional intensity function can be treated as the instantaneous emission rate observed by an ideal single-electron detector since a given starting time. We demonstrate the method by studying the instantaneous emission rate of a single-channel quantum point contact driven by a constant voltage. As the quantum point contact is opened up, we show that the emission process evolves from a simple Poisson process close to pinch-off to a non-renewal process at full transmission. These results shows that the conditional intensity function can provide an intuitive and unified description of the emission process in quantum-coherent conductors.