Full counting statistics in the not-so-long-time limit

TL;DR

This paper investigates finite measuring time corrections to the full counting statistics in interacting Fermi systems, revealing universal logarithmic behavior and analyzing effects near a charge fractionalization phase transition.

Contribution

It introduces a conjecture that finite time corrections are logarithmic with a universal coefficient and provides numerical evidence using the self-dual interacting resonant level model.

Findings

Finite time corrections are logarithmic in measuring time.

The universal coefficient relates to the long-time limit of the CGF.

Features in CGF evolution signal the charge fractionalization phase transition.

Abstract

The full counting statistics of charge transport is the probability distribution $p_n(t_m)$ that $n$ electrons have flown through the system in measuring time $t_m$. The cumulant generating function (CGF) of this distribution $F(\chi,t_m)$ has been well studied in the long time limit $t_m\rightarrow \infty$, however there are relatively few results on the finite measuring time corrections to this. In this work, we study the leading finite time corrections to the CGF of interacting Fermi systems with a single transmission channel at zero temperature but driven out of equilibrium by a bias voltage. We conjecture that the leading finite time corrections are logarithmic in $t_m$ with a coefficient universally related to the long time limit. We provide detailed numerical evidence for this with reference to the self-dual interacting resonant level model. This model further contains a phase transition associated with the fractionalisation of charge at a critical bias voltage. This transition manifests itself technically as branch points in the CGF. We provide numerical results of the dependence of the CGF on measuring time for model parameters in the vicinity of this transition, and thus identify features in the time evolution associated with the phase transition itself.