Current noise near to the 2D superconductor-insulator quantum critical point

We consider current fluctuations near to the two-dimensional superconductor-insulator transition described by a quantum XY model. This model displays metallic conductivity at criticality. We consider the system both in thermal equilibrium and when a large electric field drives it far from thermodynamic equilibrium. As the strength of the electric field is increased, we find a crossover from thermal, Johnson-Nyquist noise (whose form is demanded by the fluctuation dissipation relation) to a high-field non-linear ``shot noise'' or Schwinger regime, where the current noise is proportional to $\sqrt{E}$ . Comparison with noise in diffusive electronic systems and the possible relevance of using noise measurements in experiments on S-I systems will be discussed.