Full counting statistics in the free Dirac theory

TL;DR

This paper derives a generalized Levitov-Lesovik formula for charge transport fluctuations in the (3+1)-dimensional free Dirac theory, confirming the extended fluctuation relation and analyzing massless cases.

Contribution

It extends the Levitov-Lesovik formula to higher dimensions and provides exact results for charge fluctuations in the free Dirac model after a local quench.

Findings

Derived the scaled cumulant generating function for charge transport.

Confirmed the extended fluctuation relation in higher dimensions.

Identified that only the first four cumulants are nonzero in the massless case.

Abstract

We study charge transport and fluctuations of the (3+1)-dimensional massive free Dirac theory. In particular, we focus on the steady state that emerges following a local quench whereby two independently thermalized halves of the system are connected and let to evolve unitarily for a long time. Based on the two-time von Neumann measurement statistics and exact computations, the scaled cumulant generating function associated with the charge transport is derived. We find that it can be written as a generalization of Levitov-Lesovik formula to the case in three spatial dimensions. In the massless case, we note that only the first four scaled cumulants are nonzero. Our results provide also a direct confirmation for the validity of the extended fluctuation relation in higher dimensions. An application of our approach to Lifshitz fermions is also briefly discussed.