Conformal invariance in out-of-equilibrium Bose-Einstein condensates governed by the Gross-Pitaevskii Equation

TL;DR

This paper investigates how density isolines in out-of-equilibrium Bose-Einstein condensates governed by the Gross-Pitaevskii Equation develop conformal invariance during turbulence transition, revealing unique behavior compared to other systems.

Contribution

It demonstrates the spontaneous emergence of conformal invariance during the transition to disorder in quantum turbulence, linking it to 4-wave interacting systems.

Findings

Density isolines become more complex as turbulence matures.

Conformal invariance emerges during the transition to a thermalized regime.

The behavior differs from systems that exhibit conformal invariance during self-organization.

Abstract

We study density isolines in quantum turbulence under the Schramm-Loewner framework using direct numerical simulations of the truncated Gross-Pitaevskii equation, in both spherical and cylindrical traps with three-dimensional dynamics. Density isolines develop increasing complexity as turbulence matures. As the systems evolves towards a thermalized regime, it spontaneously develops conformal invariance. In contrast to other systems exhibiting conformal invariance, this system manifests it during the transition towards disorder rather than to self-organization. We discuss a link between this behavior in quantum turbulence and other 4-wave interacting systems.