Non-equilibrium conductivity at quantum critical points

Quantum criticality provides an important route to revealing universal non-equilibrium behaviour. A canonical example of a quantum critical point is the Bose-Hubbard model, which we study under the application of an electric field. A Boltzmann transport formalism and $\epsilon$-expansion are used to obtain the non-equilibrium conductivity and current noise. This approach allows us to explicitly identify how a universal non-equilibrium steady state is maintained, by identifying the rate-limiting step in balancing Joule heating and dissipation to a heat bath. It also reveals that the non-equilibrium distribution function is very far from a thermal distribution.