# Improved low-dimensional wave equations for cigar-shaped and disk-shaped dipolar Bose-Einstein condensates

## TL;DR

This paper derives improved low-dimensional equations for dipolar Bose-Einstein condensates with arbitrary polarization, accurately predicting ground states and outperforming standard reductions.

## Contribution

It introduces a variational ansatz-based method for deriving effective 1D and 2D equations that better approximate 3D results for dipolar BECs.

## Key findings

- Accurately predicts ground state densities.
- Strong agreement with 3D results even outside strict regimes.
- Significant improvement over standard reductions.

## Abstract

Within the formalism of the Gross-Pitaevskii equation, we derive effective one- and two-dimensional equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. These are based on an ansatz for the condensate wavefunction whose width in the tightly-confined direction/s is treated variationally. The equations constitute a coupled partial differential for the low-dimensional wavefunction and algebraic equations for the width parameters. This approach accurately predicts the ground state densities of cigar-shaped and pancake-shaped dipolar Bose-Einstein condensates, and gives strong agreement with the three-dimensional results, even as the trapping is relaxed away from the strict quasi-one- and quasi-two-dimensional regimes. This approach offers a significant improvement over the standard one- and two-dimensional reduction.