W. Belzig et Yv. Nazarov, Full counting statistics of electron transfer between superconductors - art. no. 197006, PHYS REV L, 8719(19), 2001, pp. 7006
We present an extension of the Keldysh-Green's function method, which allow
s one to calculate the full distribution of transmitted particles through a
mesoscopic superconductor. The method is applied to the statistics of supe
rcurrent in short contacts. If the current is carried by Andreev bound stat
es the distribution corresponds to switching between long trains of electro
ns going in opposite directions. For weak (gapless) superconductors or tunn
el junctions we find that at low temperatures the distribution has negative
"probabilities." Accounting for the quantum mechanical nature of the measu
ring device shows that these negative values can indeed be measured.