New classic equations for conductivity and thermopower

Abstract

All classical equations of kinetic coefficients in physics give only the first response to the external forces and fields. We have constructed new equations for kinetic coefficients, with all responses of the fields and forces, by using the perturbation method, which, customarily, was a mathematical tool for the approximate solution of the equations. Naturally, the recurrent equations which were obtained lead to recurrent solutions, which were found by the Green's function technique. The exact analytical formulae, produced by this method, play the same role for the calculations of kinetic coefficients as the Kirchhoff system of equations does for conductivity. In the framework of this solution one has obtained the upper boundary for fields when the solution is yet converged. We have considered the Hall and Seebeck coefficients and the elastic moduli (Skal A S 1997 Physica A to be published), and suggested that all other kinetic and transport coefficients may be rewritten in this way. On the basis of the formulae obtained, numerical calculations of the Hall and Seebeck coefficients are presented. The new universality classes for the Hall and Seebeck coefficients and the upper bond of the critical Hall conductivity exponent for all orders of a magnetic field contributions are obtained.