An important set of questions in condensed matter relate to the effect of nonequilibrium drives on systems near quantum critical points. Simple scaling analysis indicate that response to an external drive is highly nonlinear in the vicinity of a quantum critical point, so that a linear response Kubo formula treatment is usually invalid.

In this talk I will present a microscopic treatment for the effect of current flow on a ferromagnetic quantum critical point and show that current flow has two important effects. One is to induce decoherence which affects the system in ways rather similar to temperature.  Second it causes a symmetry breaking which leads to new terms in the critical theory. In the disordered phase and for Ising systems decoherence is the dominant effect, with inversion symmetry breaking giving only subleading corrections to scaling.  On the other hand for models with continuous rotation symmetry, current flow can lead to dynamical instabilities of the ordered phase.