Criticality in transport through the quantum Ising chain
  We consider thermal transport between two reservoirs coupled by a quantum Ising chain as a model for non-equilibrium physics induced in quantum-critical many-body systems. By deriving rate equations based on exact expressions for the quasiparticle pairs generated during the transport, we observe signatures of the underlying quantum phase transition in the steady-state energy current already at finite reservoir temperatures. 
Malte Vogl, Gernot Schaller, and Tobias Brandes
cond-mat.stat-mech quant-ph