Green’s Function Methods: Quantum Boltzmann Equation for Linear Transport

Abstract

Transport is called linear if the current is proportional to the driving force. The forces might be electric fields F, temperature gradients ∇T, or density gradients ∇n. Examples of linear transport relations are j = σF or Q = K (∇T), where the currents j (electrical) or Q (heat) are determined in terms of macroscopic coefficients σ (electrical conductivity) or K (thermal conductivity). These coefficients can be measured experimentally and calculated theoretically, which provides the meeting ground between experiment and theory. The theoretical calculation of σ and K can be done by using equilibrium Green’s functions.^(1–2) A set of theoretical techniques for linear transport, based on equilibrium Green’s functions, have been developed and are widely used.