Self-Similar acoustic white hole solutions in Bose-Einstein condensates and their Borel analysis

TL;DR

This paper investigates self-similar solutions in Bose-Einstein condensates to model acoustic white holes, analyzing their properties with Borel resummation and transseries to understand sonic horizons and flow dynamics.

Contribution

It introduces singular self-similar solutions of the Gross-Pitaevskii equation in 2D and 3D and applies Borel analysis to study their asymptotic behavior.

Findings

Identification of sonic horizons in BEC flows

Application of Borel resummation to asymptotic series

Numerical validation of self-similar solutions

Abstract

In this article, we study Self-Similar configurations of non-relativistic Bose-Einstein condensate (BEC) described by the Gross-Pitaevskii Equation (GPE). To be precise, we discuss singular Self-similar solutions of the Gross-Pitaevskii equation in 2D (with circular symmetry) and 3D (with spherical symmetry). We use these solutions to check for the crossover between the local speed of sound in the condensate and the magnitude of the flow velocity of the condensate, indicating the existence of a supersonic region and thus a sonic analog of a black/white hole. This is because phonons cannot go against the condensate flow from the supersonic to the subsonic region in such a system. We also discuss numerical techniques used and study the semi-analytical Laplace-Borel resummation of asymptotic series solutions while making use of the asymptotic transseries to justify the choice of numerical and semi-analytical approaches taken.