Full Counting Statistics as the Geometry of Two Planes

Provided the measuring time is short enough, the full counting statistics (FCS) of the charge pumped across a barrier as a result of a series of voltage pulses are shown to be equivalent to the geometry of two planes. This formulation leads to the FCS without the need for the usual non-equilibrium (Keldysh) transport theory or the direct computation of the determinant of an infinite-dimensional matrix. In the particular case of the application of N Lorentzian pulses, we show the computation of the FCS reduces to the diagonalization of an N x N matrix. We also use the formulation to compute the core-hole response in the X-ray edge problem and the FCS for a square wave pulse-train for the case of low transmission.