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

TL;DR

This paper applies the quasiclassical Green's function method to analyze equilibrium properties of one-dimensional interacting Fermi systems, providing a novel approach that aligns with established Luttinger liquid results and exploring further applications.

Contribution

It introduces a new quasiclassical Green's function approach to 1D systems, offering an alternative to bosonization for studying Luttinger liquids.

Findings

Results agree with standard Luttinger liquid theory

Established analogy with $P(E)$ tunneling theory

Discussed potential for further applications

Abstract

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.