Electrodynamics of Vortices in Quasi-2D Scalar Bose-Einstein Condensates

TL;DR

This paper establishes a duality between vortices in quasi-2D scalar Bose-Einstein condensates and effective Maxwell electrodynamics, extending the description beyond the point-vortex approximation to include dissipation and rotation.

Contribution

It introduces a novel duality mapping from vortex dynamics in BECs to 2D electrodynamics, applicable to inhomogeneous, time-dependent systems with dissipation or rotation.

Findings

Maps vortex dynamics to 2D electrodynamics beyond point-vortex approximation

Applicable to inhomogeneous, time-dependent BECs with dissipation or rotation

Provides physical interpretation of the duality

Abstract

In two spatial dimensions, vortex-vortex interactions approximately vary with the logarithm of the inter-vortex distance, making it possible to describe an ensemble of vortices as a Coulomb gas. We introduce a duality between vortices in a quasi-two-dimensional (quasi-2D) scalar Bose-Einstein condensates (BEC) and effective Maxwell's electrodynamics. Specifically, we address the general scenario of inhomogeneous, time-dependent BEC number density with dissipation or rotation. Starting from the Gross-Pitaevskii equation (GPE), which describes the mean-field dynamics of a quasi-2D scalar BEC without dissipation, we show how to map vortices in a quasi-2D scalar BEC to 2D electrodynamics beyond the point-vortex approximation, even when dissipation is present or in a rotating system. The physical meaning of this duality is discussed.