Transport in quantum chains under strong monitoring

We study the transport properties of quantum 1D systems under strong monitoring. The quantum Zeno effect inhibits transport and induces localization. Beyond the Zeno freezing and on long time scales, a new dynamics emerges in the form of a Markov process. Studying fermionic and bosonic chains under strong monitoring, we are able to identify the quantum origin of the classical exclusion process, inclusion process and a sub-class of the misanthrope process. Moreover, we show that passive monitoring cannot break time-reversal symmetry and that the transport generally loses its ballistic nature existing for weak measurements.