Improved Variational Principles for Transport Coefficients

Abstract

A sequence of variational principles for converting a trial solution of a linearized Boltzmann equation into bounds on a transport coefficient is presented. For systems in which the Boltzmann collision operator has a bounded eigenvalue spectrum, we obtain an infinite sequence of lower bounds which begins with the familiar result of Ziman. For an arbitrary trial function, this sequence converges monotonically to the exact transport coefficient. Application of the first two terms has been made to the lattice thermal conductivity of a model simulating solid argon; the second bound lies considerably higher than the first.