Correlated Gaussian Approach to Anisotropic Resonantly Interacting Few-Body Systems

TL;DR

This paper introduces a variational method using correlated Gaussian functions to study anisotropic few-body quantum systems during dimensional transitions, revealing universal behaviors in binding energies.

Contribution

It develops a numerical approach to describe few-body systems in anisotropic traps across dimensional crossovers, extending analytical solutions to non-integer dimensions.

Findings

Binding energies show universal behavior during dimensional transitions.

Configurations of bosonic and heteronuclear systems are characterized across dimensions.

Avoided crossings and Zeldovich rearrangements are observed in energy spectra.

Abstract

Quantum mechanical few-body systems in reduced dimensionalities can exhibit many interesting properties such as scale-invariance and universality. Analytical descriptions are often available for integer dimensionality, however, numerical approaches are necessary for addressing dimensional transitions. The Fully-Correlated Gaussian method provides a variational description of the few-body real-space wavefunction. By placing the particles in a harmonic trap, the system can be described at various degrees of anisotropy by squeezing the confinement. Through this approach, configurations of two and three identical bosons as well as heteronuclear (Cs-Cs-Li and K-K-Rb) systems are described during a continuous deformation from three to one dimension. We find that the changes in binding energies between integer dimensional cases exhibit a universal behavior akin to that seen in avoided crossings or Zeldovich rearrangement.