Abstract

We propose a new theoretical method to describe the monitored dynamics of many-body systems based on the concept of the most likely trajectory. We show how such a trajectory can be identified from the probability distribution of quantum trajectories, i.e., measurement readouts, and how it successfully captures the monitored dynamics beyond the average state. We prove the method to be exact in the case of Gaussian bosonic theories and then extend it to the interacting models, specifically the Sine-Gordon model. Although no longer exact in this framework, the method captures the dynamics through a self-consistent time-dependent harmonic approximation and reveals an entanglement phase transition in the steady state from an area-law to a logarithmic-law scaling.