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Universal driven dynamics near phase transitions : Kibble-Zurek ramps with and without an order parameter

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Near a critical
point, the equilibrium relaxation time of a system diverges and any change of control parameters leads to non-equilibrium behavior. The Kibble-Zurek (KZ) problem is to determine

the evolution of the system when the change is slow. In this talk, I will introduce a non-equilibrium scaling limit in which these evolutions are universal and define a KZ universality classification with exponents and scaling functions. I will illustrate the physics accessible in this

scaling limit in simple classical and quantum model theories with symmetry-breaking transitions.

I will then turn to the KZ problem near quantum phase transitions without a local order parameter.

First, I will introduce the necessary background through the example of the Ising gauge  theory/generalized toric code. Using duality and the scaling theory developed in the first part of the talk, I will then argue that the late time dynamics exhibits a slow coarsening of the string-net

that is condensed in the starting topologically ordered state. I will also discuss a time dependent amplification of the energy splitting between topologically degenerate states on closed manifolds and the dangerous irrelevance of gapped modes. Finally, I will extend these ideas to the non-abelian SU(2)_k ordered phases of the relevant Levin-Wen models.