The General Theory of Transport: The Difference between Electric Field and Density Gradient

Abstract

The difference between the electric currents due to the external electric field and the gradient of the chemical potential is discussed based on the general theory of transport coefficients. In the limit of weak magnetic field (\(\hbar{w}\ll{\kappa}T\), where ω is Larmor frequency, κ Boltzmann constant, T absolute temperature) and weak collision (\(\hbar\)/τ≪κ T , where τ means the relaxation time), Einstein relation is applicable. In the limit of strong magnetic field, the current due to the gradient of the chemical potential exhibits the oscillatory behaviour similar to that of diamagnetism.