Dimension reduction for rotating Bose-Einstein condensates with anisotropic confinement

TL;DR

This paper rigorously derives effective lower-dimensional models for rotating Bose-Einstein condensates under anisotropic confinement, revealing how rotation and anisotropy influence the condensate's behavior and effective potentials.

Contribution

It provides a rigorous mathematical derivation of reduced models for rotating BECs with anisotropic traps, including effects of rotation axis orientation.

Findings

Effective 1D and 2D equations obtained from 3D Gross-Pitaevskii equation.

Discovery of a negative quadratic potential due to rotation, acting as a centrifugal force.

Inclusion of anisotropic confinement effects in the reduced models.

Abstract

We consider the three-dimensional time-dependent Gross-Pitaevskii equation arising in the description of rotating Bose-Einstein condensates and study the corresponding scaling limit of strongly anisotropic confinement potentials. The resulting effective equations in one or two spatial dimensions, respectively, are rigorously obtained as special cases of an averaged three dimensional limit model. In the particular case where the rotation axis is not parallel to the strongly confining direction the resulting limiting model(s) include a negative, and thus, purely repulsive quadratic potential, which is not present in the original equation and which can be seen as an effective centrifugal force counteracting the confinement.