Dielectric interpretation of Lei-Ting nonlinear force-momentum–balance transport equation for isothermal resistivity

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Abstract
A dielectric interpretation of the nonlinear Lei-Ting force-momentum–balance transport equation for steady-state dc current flow is developed here in correspondence with standard techniques for calculating fast-particle energy loss to a plasmalike medium. In conjunction with this we interpret the result to be an isothermal resistivity calculated to lowest order in the impurity scattering potentials, isothermal in the sense that all energy dissipated is removed from the system, essentially instantaneously as it is generated, by a heat bath in contact with the system which maintains it at constant temperature throughout the nonlinear dc conduction process. On the basis of its isothermal character, we argue that the Lei-Ting dc resistivity calculated to lowest order in the impurity scattering potentials—whose linear limit is significantly different from the corresponding linear resistivity of an adiabatic character (for a system admitting no drainoff of dissipated energy, developing under a purely mechanical Hamiltonian)—is immune to serious critical objections of the type brought by Argyres and Sigel against similar lowest-order adiabatic linear resistivity calculations some time ago. Moreover, we also show that a dielectric Lei-Ting type formulation of linearized ac resistivity leads to the standard high-frequency linear resistivity formula, and that its zero-frequency limit naturally yields the isothermal dc linear Lei-Ting resistivity.