Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit

Within a hydrodynamic framework, the authors describe the out-of-equilibrium dynamics of noninteracting one-dimensional fermionic systems, featuring localized gain and loss of particles at the center of the system. They discuss quenches from equilibrium and nonequilibrium homogeneous initial states as well as from inhomogeneous ones. The results demonstrate the existence of a Zeno effect for large loss rates and the emergence of exotic nonequilibrium steady states with a stepwise uniform density profile that is discontinuous in correspondence with the localized loss.