Atomic arrays as open quantum systems: scalability and steady-state order

I will discuss universal scaling laws for the maximal decay rate of many-body quantum systems and their implications for the scalability of quantum processors and simulators, where collective decay may impose fundamental limits through correlated errors. I will then show that these scaling laws are governed by the optical depth of the array, which emerges as the unifying physical parameter linking ordered and disordered ensembles. Finally, I will discuss steady-state behavior in one-dimensional reservoirs, where correlated decay and incoherent pumping together give rise to spin order and steady-state superradiance beyond the Dicke limit.