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

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