Full Counting Statistics as the Geometry of Two Planes

Abstract

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.

4 pages, 1 figure

References in corpus (8)

• Electron Counting Statistics and Coherent States of Electric Current
• Minimal excitation states of electrons in one-dimensional wires
• Electron shot noise beyond the second moment
• Coherent States of Alternating Current,
• Counting statistics of photons produced by electronic shot noise
• Elementary events of electron transfer in a voltage-driven quantum point contact
• Allowed charge transfers between coherent conductors driven by a time-dependent scatterer
• Fermi gas response to time-dependent perturbations

Cited by in corpus (4)

• Elementary Charge Transfer Processes in Mesoscopic Conductors
• Factorization of quantum charge transport for non-interacting fermions
• Optimal electron entangler and single electron source at low temperatures
• Full Counting Statistics of Quantum Point Contact with Time-dependent Transparency