# Fluctuating hydrodynamics, current fluctuations and hyperuniformity in boundary-driven open quantum chains

## TL;DR

This paper develops a fluctuating hydrodynamics framework for boundary-driven open quantum chains, revealing a third-order dynamical phase transition and hyperuniform rare trajectories, supported by numerical simulations.

## Contribution

It introduces a hydrodynamic description for quantum chains with boundary dissipation, enabling analysis of current fluctuations and phase transitions.

## Key findings

- Fermionic chains exhibit a third-order dynamical phase transition.
- Rare trajectories are ballistic and hyperuniform.
- Numerical methods confirm analytical predictions.

## Abstract

We consider a class of either fermionic or bosonic noninteracting open quantum chains driven by dissipative interactions at the boundaries and study the interplay of coherent transport and dissipative processes, such as bulk dephasing and diffusion. Starting from the microscopic formulation, we show that the dynamics on large scales can be described in terms of fluctuating hydrodynamics. This is an important simplification as it allows us to apply the methods of macroscopic fluctuation theory to compute the large deviation (LD) statistics of time-integrated currents. In particular, this permits us to show that fermionic open chains display a third-order dynamical phase transition in LD functions. We show that this transition is manifested in a singular change in the structure of trajectories: while typical trajectories are diffusive, rare trajectories associated with atypical currents are ballistic and hyperuniform in their spatial structure. We confirm these results by numerically simulating ensembles of rare trajectories via the cloning method, and by exact numerical diagonalization of the microscopic quantum generator.