Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime

TL;DR

This paper derives reduced-dimensional models for dipolar Bose-Einstein condensates in strong interaction regimes, using averaging and semiclassical methods to analyze disk and cigar shaped geometries.

Contribution

It introduces asymptotic models for dipolar BECs with explicit convergence rates, extending understanding of dimension reduction in anisotropic, long-range interacting quantum gases.

Findings

Derived asymptotic models with convergence rates

Analyzed dimension reduction from 3D to 2D and 1D

Combined averaging and semiclassical techniques

Abstract

We study dimension reduction for the three-dimensional Gross-Pitaevskii equation with a long-range and anisotropic dipole-dipole interaction modeling dipolar Bose-Einstein condensation in a strong interaction regime. The cases of disk shaped condensates (confinement from dimension three to dimension two) and cigar shaped condensates (confinement to dimension one) are analyzed. In both cases, the analysis combines averaging tools and semiclassical techniques. Asymptotic models are derived, with rates of convergence in terms of two small dimensionless parameters characterizing the strength of the confinement and the strength of the interaction between atoms.