Spatiotemporal chaos and extended self-similarity of Bose-Einstein condensates in a one-dimensional harmonic trap

We investigate spatiotemporal chaos in Bose-Einstein condensate (BEC) confined by a one-dimensional 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-type scaling through extended self-similarity (ESS). Our findings suggest that ESS and density structure functions provide experimentally accessible tools to explore spatiotemporal chaos and turbulencelike behavior in BECs.