Current fluctuations in the transient regime: An exact formulation for mesoscopic systems

We report a theoretical analysis of current-current correlations in an arbitrary noninteracting mesoscopic phase-coherent device connected to arbitrary noninteracting external leads, in response to the sharp turning off of the bias voltage. Based on the Keldysh nonequilibrium Green's function formalism, we provide an exact analytical solution to the time-dependent current-current correlations in the far from equilibrium, nonlinear response regime. An important feature of our theory is that it does not rely on the commonly used wideband approximation so that the full electronic structure of the device leads is taken into account. As such, our theory provides a way to perform calculations of transient current fluctuations from first principles on realistic systems. We apply the exact formulation to a two-probe transport junction with the Lorentzian linewidth and investigate the time-dependent behavior of the current-current correlations when the voltage bias is abruptly turned off.