The Statistical Theory of Mesoscopic Noise

Abstract

Microscopic theory of counting statistics of electrical noise is reviewed. We discuss a model of passive charge detector based on current fluctuations coupled to a spin, and its relation with the theory of photon counting in quantum optics. The statistics of tunneling current and, in particular, the properties of the third moment are studied in detail. The third moment is shown to be temperature-independent for tunneling in a generic many-body system. Then the statistics of mesoscopic transport is discussed. We consider applications of the functional determinant formula for the generating function of counting distribution to the DC and photo-assisted transport, and to mesoscopic pumping. A universal dependence of the noise in a mesoscopic pump on the pumping fields is obtained and shown to provide a method of measuring the quasiparticle charge in an open system without any fitting parameters.