Full Counting Statistics as the Geometry of Two Planes

TL;DR

This paper introduces a geometric approach to full counting statistics (FCS) for charge transport, simplifying calculations by avoiding complex non-equilibrium theories and enabling efficient analysis for specific pulse shapes.

Contribution

It presents a novel geometric formulation of FCS that simplifies calculations and applies to various pulse types without traditional complex methods.

Findings

FCS can be represented as the geometry of two planes for short measurement times.

The method simplifies FCS calculation to matrix diagonalization for Lorentzian pulses.

Application to X-ray edge problem and square wave pulses demonstrates versatility.

Abstract

Provided the measuring time is short enough, the full counting statistics (FCS) of the charge pumped across a barrier as a result of a series of voltage pulses are shown to be equivalent to the geometry of two planes. This formulation leads to the FCS without the need for the usual non-equilibrium (Keldysh) transport theory or the direct computation of the determinant of an infinite-dimensional matrix. In the particular case of the application of N Lorentzian pulses, we show the computation of the FCS reduces to the diagonalization of an N x N matrix. We also use the formulation to compute the core-hole response in the X-ray edge problem and the FCS for a square wave pulse-train for the case of low transmission.