Singularity formation in the Gross-Pitaevskii Equation and Collapse in BEC

TL;DR

This paper investigates the collapse mechanism of Bose-Einstein condensates described by the Gross-Pitaevskii equation, focusing on how initial conditions and dissipation influence condensate collapse and remnant fractions.

Contribution

It introduces a reformulation of the Gross-Pitaevskii equation as Newton's equations and models particle expulsion during collapse, providing new insights into collapse dynamics.

Findings

Collapse depends on initial aspect ratio and scattering length.

Dissipation affects the expelled particle fraction.

Remnant condensate size varies with initial conditions.

Abstract

We study a mechanism of collapse of the condensate wave function in the Gross-Pitaevskii theory with attractive interparticle interaction. We reformulate the Gross-Pitaevskii equation as Newton's equations for the particle flux and introduce a collapsing fraction of particles. We assume that the collapsing fraction is expelled from the condensate due to dissipation. Using this hypothesis we analyze the dependence of the condensate collapse on the initial conditions. We found that for a properly chosen negative scattering length the remnant fraction becomes larger when the initial aspect ratio is increased.