Topological mixed quantum states in or out of equilibrium can arise in open quantum systems. Their linear responses are generally non-quantized, even though quantized topological invariants can be defined. In this talk, I will present a real-time U(1) topological gauge field action capable of reconciling this paradoxical phenomenology. In addition to non-quantized linear responses, this action encodes quantized non-linear responses associated with mixed state topology. Also, this construction demonstrates how the physical pictures of anomaly inflow and bulk-boundary correspondence extend to non-equilibrium systems.

(Pizza and refreshments will be served after the talk.)