# Transmission coefficient of interacting few-body system in one dimensional space

## TL;DR

This paper introduces a new formalism for defining the transmission coefficient in one-dimensional systems with interacting electrons, linking it to the unitarity of the scattering matrix and comparing it to the Landauer-Büttiker approach.

## Contribution

It proposes a novel method for calculating transmission in interacting systems, extending the understanding of transport beyond non-interacting models.

## Key findings

- Formalism based on unitarity of the S-matrix
- Relation to Landauer-Büttiker formula established
- Transport properties of two-electron system analyzed

## Abstract

We present a novel way of defining transmission coefficient of one spatial dimensional few interacting electrons system. The formalism is based on the probability interpretation of unitarity of physical scattering $S$-matrix. The relation of our formalism to the well-established method for describing the conducting properties of non-interacting systems, Landauer-B\"uttiker formula, is discussed. The transport properties of interacting two-electron system is also discussed as a specific example of our formalism.