Hyperspherical Treatment of Strongly-Interacting Few-Fermion Systems in One Dimension

TL;DR

This paper explores a hyperspherical approach to analyze strongly interacting two-component fermions in one dimension, providing insights into few-body systems and their energy behaviors under strong repulsive interactions.

Contribution

It introduces a hyperspherical formalism for treating strongly interacting one-dimensional fermionic systems, including a detailed analysis of three-body and N-body energy behaviors.

Findings

Hyperspherical formalism effectively describes three-fermion systems in a trap.

Energy behavior of N-body systems under strong interactions analyzed.

Method offers a new perspective on strongly correlated one-dimensional fermions.

Abstract

We examine a one-dimensional two-component fermionic system in a trap, assuming that all particles have the same mass and interact through a strong repulsive zero-range force. First we show how a simple system of three strongly interacting particles in a harmonic trap can be treated using the hyperspherical formalism. Next we discuss the behavior of the energy for the N-body system.