Stability, effective dimensions, and interactions for bosons in deformed fields

TL;DR

This paper uses the hyperspherical adiabatic method to analyze the stability of Bose-Einstein condensates in deformed traps, revealing how geometry influences effective dimensions and stability criteria.

Contribution

It provides analytical approximations for stability conditions of bosons in deformed fields and introduces a dimension-dependent effective Hamiltonian.

Findings

Maximum stability occurs in spherical traps at constant volume.

Deformation causes the system to effectively behave in lower dimensions.

The effective radial Hamiltonian varies continuously with deformation.

Abstract

The hyperspherical adiabatic method is used to derive stability criteria for Bose-Einstein condensates in deformed external fields. An analytical approximation is obtained. For constant volume the highest stability is found for spherical traps. Analytical approximations to the stability criterion with and without zero point motion are derived. Extreme geometries of the field effectively confine the system to dimensions lower than three. As a function of deformation we compute the dimension to vary continuously between one and three. We derive a dimension-dependent effective radial Hamiltonian and investigate one choice of an effective interaction in the deformed case.