Symmetry Breaking in Quantum and Classical Open System Dynamics

In generic open quantum systems, universal dynamical processes tend to exhibit classicality - dissipation washes out quantum effects. Here I consider open quantum dynamics in the presence of a global U(1) symmetry. In mixed states, this symmetry can be either strong or weak, and distinct dynamical phases can be characterized by the spontaneous breaking of either symmetry. The strong-to-weak spontaneous symmetry breaking (SW-SSB) transition is characterized by various information theoretic quantities which are non-linear in the system's mixed state density matrix. Within a Lindblad framework for U(1) dynamics, we show that a finite-time SW-SSB transition occurs in two and three dimension, whereas in one dimension the correlation length grows linearly with time and diverges only in the infinite-time steady state. Moreover, with carefully chosen Lindblad dynamics, the SW-SSB transition signals a finite time breakdown of quantum dynamics, giving rise to classical dynamics described by a stochastic Langevin equation (Model F of Halperin-Hohenberg). When the weak symmetry is spontaneously broken, the system enters a superfluid state with classical hydrodynamics. I will comment on the prospects of observing the SW-SSB transition in cold atomic gas simulators, as revealed by an appropriately chosen quantum-classical cross-correlator.