Dynamics of the relativistic Gross-Pitaevskii equation with harmonic potential: Following the variational approach

TL;DR

This paper investigates the dynamics of the relativistic Gross-Pitaevskii equation with a harmonic potential, using a variational approach to explore collective excitations and free expansion in a relativistic Bose-Einstein condensate.

Contribution

It introduces a relativistic extension of the Gross-Pitaevskii equation with a harmonic trap, employing the Higgs model and variational methods to analyze mode coupling and confinement effects.

Findings

Identified nonlinear coupling between dipolar and monopolar modes.

Showed free expansion transitions from ballistic to relativistic confinement.

Provided insights into relativistic effects on Bose-Einstein condensate dynamics.

Abstract

The role of the collective excitations as well as the free expansion dynamics provide a key diagnostic tools for trapped Bose-Einstein condensations. Based on such dynamics we proposed to study the relativistic version of them in the context of a macroscopic occupation of the ground-state for spin-0 particles. Therefore we used the Higgs model where the external trap is introduced by a non-minimal coupling. Along with variational method, we obtained a nonlinear coupling between dipolar and monopolar modes. Furthermore, the free expansion is no longer ballistic reaching a relativistic confinement.