Unidimensional reduction of the 3D Gross-Pitaevskii equation with two- and three-body interactions

TL;DR

This paper derives a simplified one-dimensional model from the 3D Gross-Pitaevskii equation for dilute bosonic gases with two- and three-body interactions, analyzing its validity through numerical simulations.

Contribution

It introduces a unidimensional reduction of the 3D Gross-Pitaevskii equation considering two- and three-body interactions, with validation via numerical analysis.

Findings

The reduced 1D equation accurately describes the system under strong confinement.

Numerical simulations confirm the validity of the reduction in specific interaction regimes.

The approach accounts for competing nonlinearities from two- and three-body interactions.

Abstract

We deal with the three-dimensional Gross-Pitaevskii equation, which is used to describe a cloud of dilute bosonic atoms that interact under competing two- and three-body scattering potentials. We study the case where the cloud of atoms is strongly confined in two spatial dimensions, allowing us to build an unidimensional nonlinear equation, controlled by the nonlinearities and the confining potentials that trap the system along the longitudinal coordinate. We focus attention on specific limits, dictated by the cubic and quintic coefficients, and we implement numerical simulations to help us to quantify the validity of the procedure.