Numerical Evaluation of Shot Noise using Real Time Simulations

TL;DR

This paper introduces a numerical method to evaluate shot noise in quantum systems using time evolution simulations, focusing on the single resonant level model to analyze finite size effects and noise characteristics.

Contribution

It develops a numerical approach to determine shot noise from time evolution data, providing benchmarks and insights into finite size effects in non-interacting quantum models.

Findings

Finite size corrections scale with the square of differential conductance

Complete characterization of zero-frequency noise and finite frequency effects

Finite damping influences noise measurements

Abstract

We present a method to determine the shot noise in quantum systems from knowledge of their time evolution - the latter being obtained using numerical simulation techniques. While our ultimate goal is the study of interacting systems, the main issues for the numerical determination of the noise do not depend on the interactions. To discuss them, we concentrate on the single resonant level model, which consists in a single impurity attached to non-interacting leads, with spinless fermions. We use exact diagonalisations (ED) to obtain time evolution, and are able to use known analytic results as benchmarks. We obtain a complete characterization of finite size effects at zero frequency, where we find that the finite size corrections scale $\propto G^2$, $G$ the differential conductance. We also discuss finite frequency noise, as well as the effects of damping in the leads.