Quasiclassical theory of electronic transport in mesoscopic systems: Luttinger liquids revisited

The method of the quasiclassical Green's function is used to determine the equilibrium properties of one-dimensional (1D) interacting Fermi systems, in particular, the bulk and the local (near a hard wall) density of states. While this is a novel approach to 1D systems, our findings do agree with standard results for Luttinger liquids obtained with the bosonization method. Analogies to the so-called $P(E)$ theory of tunneling through ultrasmall junctions are pointed out and are exploited. Further applications of the Green's function method for 1D systems are discussed.