Analysis of universality in transient dynamics of coherent electronic transport

TL;DR

This paper investigates the universal features of charge transfer statistics in quantum dots during transient dynamics, providing numerical and analytical tools to understand short-time behavior in coherent electronic transport.

Contribution

It introduces a numerical method for evaluating the full-counting statistics and derives an analytic expression linking cumulants to zeros of the generating function, revealing short-time universality.

Findings

Short-time universality due to a dominant zero in the generating function

Analytic expression for all order cumulants at any time

Robustness of universal features in both sequential and coherent regimes

Abstract

We analyze the time-dependent full-counting statistics of charges transmitted through a quantum dot in the coherent regime. The generating function for the time-dependent charge transfer statistics is evaluated numerically by discretizing the Keldysh time contour, which allows us to compute the higher order charge and current cumulants. We also develop an analytic expression for all order cumulants at any time given as a function of the zeros of the generating function, finding that the short time universality is due to the presence of a dominant single zero. The robustness of the universal features at short times is studied in both the sequential and coherent regimes.