Generalized Mobility Theory

A formal theory of mobility is presented that does not depend on the existence of a transport equation. In particular the Hamiltonian describing the electron plus scattering system is not decomposed into an unperturbed part plus a perturbation. Only the applied field is treated as small. Our result is shown to reduce to the usual transport result when the scattering perturbation is weak, without assuming the existence of a relaxation time. Further verification of the validity of our result is obtained by using it to demonstrate a complex Nyquist theorem. Mathematical convergence factors introduced in previous theories are shown to arise naturally here by allowing a weak interaction between the electron plus scattering systems and the universe. The relation between a many-electron treatment and the one-electron treatment is demonstrated for the case of Fermi as well as Boltzmann statistics.