Electron Waiting Times in Mesoscopic Conductors

TL;DR

This paper develops a quantum theoretical framework for electron waiting times in mesoscopic conductors, revealing how electron timing statistics transition between different regimes and highlighting the wave nature of electrons even in noiseless transport.

Contribution

It introduces a determinant formula for electron waiting time distributions in mesoscopic conductors, bridging a gap in the theoretical understanding of charge transport.

Findings

Waiting time distribution transitions from Wigner-Dyson to Poisson statistics.

Electrons are not equally spaced in time despite noiseless low-frequency transport.

Analogies are drawn between electron waiting times and energy level statistics.

Abstract

Electron transport in mesoscopic conductors has traditionally involved investigations of the mean current and the fluctuations of the current. A complementary view on charge transport is provided by the distribution of waiting times between charge carriers, but a proper theoretical framework for coherent electronic systems has so far been lacking. Here we develop a quantum theory of electron waiting times in mesoscopic conductors expressed by a compact determinant formula. We illustrate our methodology by calculating the waiting time distribution for a quantum point contact and find a cross-over from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off. Even when the low-frequency transport is noiseless, the electrons are not equally spaced in time due to their inherent wave nature. We discuss the implications for renewal theory in mesoscopic systems and point out several analogies with energy level statistics and random matrix theory.