Simple holographic model of nonlinear conductivity
gary@physics.ucsb.edu, niqbal@kitp.ucsb.edu, jss55@physics.ucsb.eduAbstractWe present a simple analytic gravitational solution which describes the holographic dual ofa 2 + 1-dimensional conductor which goes beyond the usual linear response. In particularit includes Joule heating. We nd that the nonlinear frequency-dependent conductivity isa constant. Surprisingly, the pressure remains isotropic. We also apply an electric eld toa holographic insulator and show that there is a maximum electric eld below which it canremain an insulator. Above this critical value, we argue that it becomes a conductor due topair creation of charged particles. Finally, we study 1+1 and 3+1 dimensional conductors atthe nonlinear level; here exact solutions are not available and a perturbative analysis showsthat the current becomes time dependent, but in a way that is captured by a time-dependent