  An isolated quantum gas with a localized loss features a non-monotonic
behavior of the particle loss rate as an incarnation of the quantum Zeno
effect, as recently shown in experiments with cold atomic gases. While this
effect can be understood in terms of local, microscopic physics, we show that
novel many-body effects emerge when non-linear gapless quantum fluctuations
become important. To this end, we investigate the effect of a local dissipative
impurity on a one-dimensional gas of interacting fermions. We show that the
escape probability for modes close to the Fermi energy vanishes for an
arbitrary strength of the dissipation. In addition, transport properties across
the impurity are qualitatively modified, similarly to the Kane-Fisher barrier
problem. We substantiate these findings using both a microscopic model of
spinless fermions and a Luttinger liquid description.
