Biittiker

Biittiker M, Imry Y, Landauer R, Pinhas S (1985) Generalized many-channel conductance formula with application to small rings. Phys Rev B 31(10) 6207... 

M. Biittiker, The Quantum Hall Effects in Open Conductors... 

Acknowledgements.— We thank C. Beenakker, W. Belzig, M. Biittiker, A. Clerck, M. Devoret, Y. Gefen, S. Girvin, N. Hengartner, M. Kindermann, L. Levitov, A. Mukherjee, Y. Nazarov and P.-E. Roche for useful discussions. This work was supported by NSF DMR 0072022. 

However, the peculiarity of single-molecule transport is just essential role of electron-electron and electron-vibron interactions, so that Landauer-Biittiker method is not enough usually to describe essential physics even qualitatively (see, however Refs. [303-305] for inelastic scattering effects). 

The physical sense of this expressions is quite transparent, they describe the quantum amplitudes of the scattering processes. Three functions scattering state in the Landauer-Biittiker theory. Note, that G here is the full GF of the nanosystem including the lead self-energies. 

It looks as simple as the Landauer-Biittiker formula, but it is not trivial, because the spectral density A(e) = —21mGR(e) now depends on the distribution function of the electrons in the fluctuating molecule and hence the applied voltage, cpR = —cpR = V/2 [123]. Indeed, GR(e) can be found from (201)... 

M. Biittiker, Absence of backscattering in the quantum Hall effect in multiprobe conductors, Phys. Rev. B38 9375-9389 (1988). 

M. Biittiker R. Landauer, in Nonlinear phenomena at phase transitions and instabilities, T. Riste (Plenum Press, New York, p. Ill, 1982). 

---