Scattering Approach to Counting Statistics in Quantum Pumps

TL;DR

This paper introduces a general method using a matrix Riemann-Hilbert problem to determine the quantum statistics of various quantities in a non-equilibrium Fermi gas, with applications to charge transfer in quantum point contacts.

Contribution

It provides a novel, general approach to compute quantum statistics in non-equilibrium states, applicable to various physical quantities and measurement scenarios.

Findings

Finite measurement time affects charge transfer distribution.

Method applicable to charge, energy, and momentum statistics.

Provides a unified framework for non-equilibrium quantum statistics.

Abstract

We consider the Fermi gas in a non-equilibrium state obtained by applying an arbitrary time-dependent potential to the Fermi gas in the ground state. We present a general method that gives the quantum statistics of any single-particle quantity, such as the charge, total energy or momentum, in this non-equilibrium state. We show that the quantum statistics may be found from the solution of a matrix Riemann-Hilbert problem. We use the method to study how the finite measuring time modifies the distribution of the charge transferred through a biased quantum point contact.