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

TL;DR

This paper provides an exact hydrodynamic description of noninteracting fermionic chains with localized gain and loss, revealing how dissipation influences quantum dynamics and steady states, including the quantum Zeno effect.

Contribution

It introduces an exact hydrodynamic framework for fermionic systems with localized dissipation, connecting microscopic dynamics to macroscopic behavior and analyzing various initial states.

Findings

Hydrodynamic description derived from microscopic dynamics.

Emergence of exotic nonequilibrium steady states.

Quantum Zeno effect suppressing coherent dynamics.

Abstract

We investigate the interplay between unitary dynamics after a quantum quench and localized dissipation in a noninteracting fermionic chain. In particular, we consider the effect of gain and loss processes, for which fermions are added and removed incoherently. We focus on the hydrodynamic limit of large distances from the source of dissipation and of long times, with their ratio being fixed. In this limit, the localized dissipation gives rise to an effective delta potential (dissipative impurity), and the time-evolution of the local correlation functions admits a simple hydrodynamic description in terms of the fermionic occupations in the initial state and the reflection and transmission amplitudes of the impurity. We derive this hydrodynamic framework from the ab initio calculation of the microscopic dynamics. This allows us to analytically characterize the effect of dissipation for several theoretically relevant initial states, such as a uniform Fermi sea, homogeneous product states, or the inhomogeneous state obtained by joining two Fermi seas. In this latter setting, when both gain and loss processes are present, we observe the emergence of exotic nonequilibrium steady states with stepwise uniform density profiles. In all instances, for strong dissipation the coherent dynamics of the system is arrested, which is a manifestation of the celebrated quantum Zeno effect.