# The one step fermionic ladder

## TL;DR

This paper develops a non-chiral bosonization technique to analytically compute Green functions for a fermionic ladder system with inhomogeneities, revealing insights into Friedel oscillations and conductance.

## Contribution

It introduces a novel non-chiral bosonization method for strongly inhomogeneous ladder systems, providing exact correlation functions including in the presence of interactions.

## Key findings

- Analytical expression for Green functions derived
- Friedel oscillations characterized in the ladder system
- Conductance behavior analyzed under potential differences

## Abstract

The one step fermionic ladder refers to two parallel Luttinger Liquids (poles of the ladder) placed such that there is a finite probability of electrons hopping between the two poles at a pair of opposing points along each of the poles. The many-body Green function for such a system is calculated in presence of forward scattering interactions using the powerful non-chiral bosonization technique (NCBT). This technique is based on a non-standard harmonic analysis of the rapidly varying parts of the density fields appropriate for the study of strongly inhomogeneous ladder systems. The closed analytical expression for the correlation function obtained from NCBT is nothing but the series involving the RPA (Random Phase Approximation) diagrams in powers of the forward scattering coupling strength resummed to include only the most singular terms with the source of inhomogeneities treated exactly. Finally the correlation functions are used to study physical phenomena such as Friedel oscillations and the conductance of such systems with the potential difference applied across various ends.