Stationary acoustic black hole solutions in Bose-Einstein condensates and their Borel analysis

TL;DR

This paper investigates stationary solutions of Bose-Einstein condensates that mimic black/white hole horizons using the Gross-Pitaevskii equation, analyzing their properties with numerical and semi-analytical methods including Borel analysis.

Contribution

It introduces singular stationary solutions in 2D and 3D BECs and applies Borel and resurgent analysis to understand their behavior and relation to acoustic black hole analogs.

Findings

Identification of conditions for sonic horizons in BEC flows

Validation of semi-analytical Borel resummation against numerical solutions

Insights into the role of transseries in BEC black hole solutions

Abstract

In this article, we study the dynamics of a Bose-Einstein condensate (BEC) with the idea of finding solutions that could possibly correspond to a so-called acoustic (or Unruh) black/white holes. Those are flows with horizons where the speed of the flow goes from sub-sonic to super-sonic. This is because sound cannot go back from the supersonic to the subsonic region. The speed of sound plays the role of the speed of light in a gravitational black hole, an important difference being that there are excitations that can go faster than the speed of sound and therefore can escape the sonic black hole. Here, the motion of the BEC is described by the Gross-Pitaevskii Equation (GPE). More concretely, we discuss singular Stationary solutions of Gross-Pitaevskii equation in 2D (with Circular symmetry) and 3D (with Spherical symmetry). We use these solutions to study the local speed of sound and magnitude of flow velocity of the condensate to see whether they cross, indicating the potential existence of a sonic analog of a black/white hole. We discuss numerical techniques used and also study the semi-analytical Laplace-Borel resummation of asymptotic series solutions to see how well they agree with numerical solutions. We also study how the resurgent transseries plays a role in these solutions.