Charge Transport at the Nanometer Scale Length from Fluctuation–Dissipation and Duality Theorems

In this paper, 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, and 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 and 1D geometry, solids and vacuum. To the purpose of comparing analogous results carried out with existing kinetic approaches, the original Drude kinetic equation of 1900 is implemented to include ballistic transport regime and to be independent of quantum and fractional exclusion statistics. Furthermore, Landauer paradigm, conductance is transmission, is here generalized with the dual paradigm, resistance is reflection of carriers between opposite contacts. Finally, relations between conductance in solid samples and vacuum are briefly reviewed.