Electrical transport in open and closed systems

Abstract

Electrical conductance is typically calculated by approaches which view the electrical field as a causative source and the motion of carriers as a response. An alternative viewpoint, which starts from the flux of carriers maintained at the edges of a sample, and then calculates how charges build up and fields develop, has gained acceptance in the treatment of disordered systems, the solid state Aharanov-Bohm effect, and universal fluctuations. We analyze some of the less appreciated concomitants of this viewpoint, emphasizing both the generality and limitations of the viewpoint. Particular emphasis is given to the Residual Resistivity Dipole; localized scatterers in metallic conductivity are accompanied by highly localized transport fields. Closed Hamiltonian systems, e.g. a metallic ring with elastic scattering and driven by a time-dependent magnetic flux, are conservative. They cannot exhibit dissipation, under our conventionally accepted forms of physics. It is suggested that the limited precision available, in principle, in calculating the behavior of physical systems limits our ability to retrieve energy from supposedly conservative systems. This can be regarded as the ultimate source of dissipative processes. © 1987 Springer-Verlag.