Delayed collapses of BECs in relation to AdS gravity

TL;DR

This paper explores the analogy between Bose-Einstein condensate collapses and AdS gravitational collapse, using numerical simulations of the Gross-Pitaevskii equation to gain insights into both phenomena.

Contribution

It demonstrates the qualitative similarity between BEC dynamics and AdS gravity collapse, providing a new perspective on nonlinear phenomena in both fields.

Findings

Wave functions bounce multiple times before collapsing

Collapse can occur even below the direct collapse threshold

Insights into resonance conditions and nonlinearity effects

Abstract

We numerically investigate spherically symmetric collapses in the Gross-Pitaevskii equation with attractive nonlinearity in a harmonic potential. Even below threshold for direct collapse, the wave function bounces off from the origin and may eventually become singular after a number of oscilla- tions in the trapping potential. This is reminiscent of the evolution of Einstein gravity sourced by a scalar field in Anti-de Sitter space where collapse corresponds to black hole formation. We carefully examine the long time evolution of the wave function for continuous families of initial states in order to sharpen out this qualitative coincidence which may bring new insights in both directions. On one hand, we comment on possible implications for the so-called Bosenova collapses in cold atom Bose-Einstein condensates. On the other hand, Gross-Pitaevskii provides a toy model to study the relevance of either the resonance conditions or the nonlinearity for the problem of Anti-de Sitter instability.