Abstract
Full-counting statistics (FCS) is an elegant method to study various fluctuations of quantities in quantum transport with generating function (GF) encoding all the distribution information. For the charge statistics, GF is expressed with respect to the modified evolution operator on the complex contour using the two-time measurement scheme, the modified evolution operator is expressed in terms of the modified Hamiltonian. Using Keldysh nonequilibrium Green’s function (NEGF) technique, GF has the form of Fredholm determinant in terms of Greens functions and self-energies in the time domain. In the long time limit, the celebrated Levitov-Lesovik’s formula and the fluctuation relation are derived from this formalism. The transient dynamics in lead-dot-lead transport system, including the cumulants of transferred charges and waiting time distribution defined under the transient regime for different temperatures is investigated numerically.
Generalizations of the formalism to the ferromagnet-normal-ferromagnet system to investigate the FCS of charge current, spin current and spin transfer torque (STT) will be presented. GFs in time domain are Fredholm determinants expressed by NEGF as well. As an application of FCS, a formalism using FCS of STT in the long time limit to calculate the switching probability of a nanomagnet system is proposed. From the stochastic Landau-Lifshitz-Gilbert (LLG) equation, the contributions to the change of the anisotropic energy, one is from the power gain due to Gilbert damping and the other is from power dissipation due to the spin transfer torque, were derived. Optimal path approximation which requires the nanomagnet to have a modestly large volume is presented and the approximation greatly reduces the numerical complexities.
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