Strongly Interacting One-Dimensional Systems with Small Mass Imbalance

TL;DR

This paper investigates how small mass differences affect the behavior and structure of strongly interacting one-dimensional bosonic systems with an impurity, revealing how trap shape influences impurity positioning and wave function degeneracy.

Contribution

It introduces an analysis of the impact of small mass asymmetry on strongly interacting 1D bosonic systems, extending previous models assuming identical masses.

Findings

Impurity position depends on trap shape and mass ratio.

Wave function degeneracy varies with mass asymmetry and trap potential.

Energy minimization shifts with impurity mass and confinement geometry.

Abstract

We study a strongly interacting system of N identical bosons and one impurity in a one-dimensional trap. First, we assume that the particles have identical masses and analyze the corresponding set-up. After that, we study the influence of a small mass asymmetry on our analysis. In particular, we discuss how the structure of the wave function and the degeneracy in the impenetrable regime depend on the mass ratio and the shape of the trapping potential. To illustrate our findings, we consider a four-body system in a box and in an oscillator. We show that in the former case the system has the smallest energy when a heavy (light) impurity is close to the edge (center) of the trap. And we demonstrate that the opposite is true in the latter case.