Classical field theory of transport of interacting classical particles through one-dimensional channels

Abstract

A classical field theory is constructed to describe the interacting classical particles in one-dimensional (1D) channels. We show the intrinsic connection between the classical field theory and the corresponding quantum theory, i.e., Tomonaga-Luttinger liquid theory, which describes the interacting fermions in 1D. As applications, we calculate the particle density function along the tube axis and the particle current through the channels by explicitly including the particle-particle and particle-wall interactions and we find quantum-classical correspondence in the conductance formula.