The MeirâÂÂWingreen formula or WeirâÂÂWingreenâÂÂJauho formula describes the electric current through an arbitrary mesoscopic system. It was formulated by Yigal Meir and Ned Wingreen, and later extended along with Antti-Pekka Jauho. It describes the current using non-equilibrium Green's functions and Keldysh formalism.
When the interaction between electrons is neglected, this formula reduces to the Landauer formula. This textbook formula has become a standard tool for calculating the current through various systems, such as molecular junctions, quantum dots and nanoscale devices.
It reads
where is the elementary charge, are the coupling matrices of the left (L) and right (R) leads, is the Keldysh Green's function, the retarded Green's function, the advanced Green's function, and the FermiâÂÂDirac distribution of lead b.