Impenetrable Mass-Imbalanced Particles in One-Dimensional Harmonic Traps

TL;DR

This paper explores the behavior of strongly interacting, mass-imbalanced particles in one-dimensional harmonic traps, developing new analytical methods to understand their properties where traditional integrability approaches fail.

Contribution

It introduces a semi-analytical hyperspherical coordinate approach for analyzing non-integrable, mass-imbalanced particle systems with strong interactions in one dimension.

Findings

Calculated energies, densities, and pair-correlation functions for four-particle mixtures.

Demonstrated the effectiveness of hyperspherical coordinates in decoupling interactions.

Provided initial steps towards understanding non-integrable mass-imbalanced systems.

Abstract

Strongly interacting particles in one dimension subject to external confinement have become a topic of considerable interest due to recent experimental advances and the development of new theoretical methods to attack such systems. In the case of equal mass fermions or bosons with two or more internal degrees of freedom, one can map the problem onto the well-known Heisenberg spin models. However, many interesting physical systems contain mixtures of particles with different masses. Therefore, a generalization of the recent strong-coupling techniques would be highly desirable. This is particularly important since such problems are generally considered non-integrable and thus the hugely successful Bethe ansatz approach cannot be applied. Here we discuss some initial steps towards this goal by investigating small ensembles of one-dimensional harmonically trapped particles where pairwise interactions are either vanishing or infinitely strong with focus on the mass-imbalanced case. We discuss a (semi)-analytical approach to describe systems using hyperspherical coordinates where the interaction is effectively decoupled from the trapping potential. As an illustrative example we analyze mass-imbalanced four-particle two-species mixtures with strong interactions between the two species. For such systems we calculate the energies, densities and pair-correlation functions.