Abstract

We study the dynamics of a monitored single particle in an one-dimensional, Anderson-localized system. The time evolution is governed by Hamiltonian dynamics for fixed time intervals, interrupted by local, projective measurements. The competition between disorder induced localization and measurement induced jumps leads to interesting behaviour of readout-averaged quantities. We find, that measurements at random positions delocalize the average position, similar to a classical random walk. Along each quantum trajectory, the particle remains localized, however with a modified localization length. In contrast to measurement induced delocalization, controlled measurements can be used to introduce transport in the system and localize the particle at a chosen site. In this sense, the measurements provide a controlled environment for the particle.