Boltzmann Description of Non-Interacting Electrons in Weakly Localized Regime

Abstract

Abstract. Transport process of non-interacting electrons is reformulated, in view of the exact treatment of interacting fermions reported by the present authors in this conference. It makes correspondence to the Boltzmann theory, covering the weakly localized regime, and also eliminates the hidden ultraviolet divergence by incorporating the particle-particle and hole-hole pairs. A mass renormalization of purely two-particle nature appears in the transport equation, giving rise to the conductivity of the Drude form. Taking the maximally crossed diagrams, the 2D conductivity is shown to vanish in the elastic scattering limit, while the distribition function preserves its sharp peak and the transport mass reduces to the free-electron value. The description differs from the self-consistent theory by Vollhardt and Wölfle, in which the Bethe-Salpeter structure of the scattering vertex is abandoned in favour of the time-reversal symmetry so the correspondence to the Boltzmann theory is lost.