Charge transport at the nano-meter scale length from fluctuation-dissipation and duality theorems

We report a microscopic interpretation of charge transport phenomena in terms of the fluctuation-dissipation theorem. Following the duality theorem recently announced by Reggiani, Alfinito, Kuhn in Phys. Rev. E 94, 032112 (2016), which interrelates carrier number and drift-velocity fluctuations under thermal equilibrium conditions, we investigate a variety of phenomena ranging from diffusive to ballistic, classical to quantum, 3D to 1D, solids to vacuum, etc. To this purpose, the original Drude kinetic equation of 1900 is implemented to include ballistic transport regime and to be independent of quantum and fractional exclusion statistics. In particular, Landauer paradigm, conductance is transmission, is here generalized with the dual paradigm resistance is reflection of carriers between opposite contacts.