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

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.