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Non-equilibrium topological matter

I will discuss two examples of topologically ordered systems out of equilibrium. In the first, the system is driven through a phase transition that reduces the topological order in the spirit of the Kibble-Zurek mechanism. When the change is slow, the non-equilibrium evolution is universal and exhibits scaling. At late times, the string-net that is condensed in the starting topological state coarsens slowly, a potentially interesting non-equilibrium signature of topological order. In the second example, quenched disorder causes the topological phase to many body localize so that the highly excited eigenstates exhibit the same topological order as the ground state. Such order would be forbidden in thermal equilibrium. I will present the arguments for and the consequences of this many-body localization in a system with discrete symmetry-protected topological order, the Haldane phase of one dimensional spin chains.