Spatiotemporal Chaos and Extended Self-Similarity of Bose Einstein Condensates in a 1D Harmonic Trap

TL;DR

This paper explores spatiotemporal chaos in Bose-Einstein condensates within a 1D harmonic trap, demonstrating Kolmogorov-like scaling and extended self-similarity through numerical simulations of the Gross-Pitaevskii equation, offering new experimental insights.

Contribution

It introduces the analysis of extended self-similarity in BECs and links chaos to turbulence-like behavior using density structure functions.

Findings

Positive Lyapunov exponents confirm chaos.

Density structure functions exhibit Kolmogorov-like scaling.

ESS provides a practical tool for experimental chaos detection.

Abstract

We investigate spatiotemporal chaos in Bose-Einstein condensate (BEC) confined by a 1D harmonic trap using Gross-Pitaevskii equation simulations. The chaos arises from nonlinear mixing of ground and excited states, confirmed by positive Lyapunov exponents. By sampling the density field at intervals matching the center-of-mass oscillation period, we analyze the density structure function. Both spatial and temporal density structure functions reveal Kolmogorov-like scaling through extended self-similarity (ESS). Our findings suggest that ESS and density structure functions provide experimentally accessible tools to explore spatiotemporal chaos and turbulence-like behavior in BECs.