Admittance and noise in an electrically driven nano-structure: Interplay between quantum coherence and statistics

We investigate the interplay between the quantum coherence and statistics in electrically driven nano-structures. We obtain expression for the admittance and the current noise for a driven nano-capacitor in terms of the Floquet scattering matrix and derive a non-equilibrium fluctuation-dissipation relation. As an interplay between the quantum phase coherence and the many-body correlation, the admittance has peak values whenever the noise power shows a step as a function of near-by gate voltage. Our theory is demonstrated by calculating the admittance and noise of driven double quantum dots.