Non-equilibrium current cumulants and moments with a point-like defect

TL;DR

This paper derives exact non-equilibrium current cumulants and moments in a quantum multi-terminal system with a point defect, revealing the full probability distribution of particle transport driven by heat reservoirs.

Contribution

It provides an exact analytical framework for current cumulants, moments, and the probability distribution in a non-equilibrium quantum transport system with a point-like defect.

Findings

Explicit expressions for current cumulants and moments.

Unique solution to the associated moment problem.

Probabilities of particle emission and absorption fully describe transport.

Abstract

We derive the exact n-point current expectation values in the Landauer-Buttiker non-equilibrium steady state of a multi terminal system with star graph geometry and a point-like defect localised in the vertex. The current cumulants are extracted from the connected correlation functions and the cumulant generating function is established. We determine the moments, show that the associated moment problem has a unique solution and reconstruct explicitly the corresponding probability distribution. The basic building blocks of this distribution are the probabilities of particle emission and absorption from the heat reservoirs, driving the system away from equilibrium. We derive and analyse in detail these probabilities, showing that they fully describe the quantum transport problem in the system.