Conformal field theory out of equilibrium: a review

Understand

We provide a pedagogical review of the main ideas and results in non-equilibrium conformal field theory and connected subjects.

• These concern the understanding of quantum transport and its statistics at and near critical points.
• Starting with phenomenological considerations, we explain the general framework, illustrated by the example of the Heisenberg quantum chain.
• We then introduce the main concepts underlying conformal field theory (CFT), the emergence of critical ballistic transport, and the CFT scattering construction of non-equilibrium steady states.