Density and current statistics in boundary-driven monitored fermionic chains

TL;DR

This paper investigates the full probability distribution of local density and current in boundary-driven monitored fermionic chains, revealing qualitative differences in typical behavior depending on monitoring strength, including signs of Zeno-like localization.

Contribution

It provides the first detailed analysis of the full distribution functions of local observables in monitored fermionic chains, highlighting the importance of typical behavior beyond average dynamics.

Findings

Median density and current profiles differ from averages under strong monitoring.

Weak monitoring shows diffusive profiles for median density and current.

Strong monitoring induces domain-wall and single-peak profiles, indicating localization.

Abstract

We consider a one-dimensional system of non-interacting fermions featuring both boundary driving and continuous monitoring of the bulk particle density. Due to the measurements, the expectation values of the local density and current operators are random variables whose average behavior is described by a well studied Lindblad master equation. By means of exact numerical computations, we go beyond the averaged dynamics and study their full probability distribution functions, focusing on the late-time stationary regime. We find that, contrary to the averaged values, the spatial profiles of the median density and current are non-trivial, exhibiting qualitative differences as a function of the monitoring strength. At weak monitoring, the medians are close to the means, displaying diffusive spatial profiles. At strong monitoring, we find that the median density and current develop a domain-wall and single-peak profile, respectively, which are suggestive of a Zeno-like localization in typical quantum trajectories. While we are not able to identify a sharp phase transition as a function of the monitoring rate, our work highlights the usefulness of characterizing typical behavior beyond the averaged values in the context of monitored many-body quantum dynamics.