Information Entropy for a Two-Dimensional Rotating Bose–Einstein Condensate

We study the information entropy, order, disorder, and complexity for the two-dimensional (2D) rotating and nonrotating Bose–Einstein condensates. The choice of our system is a complete theoretical laboratory where the complexity is controlled by the two-body contact interaction strength and the rotation frequency (Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega $$\end{document}) of the harmonic trap. The 2D nonrotating condensate shows the complexity of the category I where the disorder-order transition is triggered by the interaction strength. In the rotating condensates, Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega $$\end{document} is chosen as the disorder parameter when the interaction strength is fixed. With respect to Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega $$\end{document}, the complexity shifts between maximum and minimum confirm the existence of category II complexity in the rotating condensate. Also, we consider the interaction strength as the disorder parameter when Ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varOmega $$\end{document} is unchanged and complexity as a function of interaction strength exhibits category III complexity. The present work also includes the calculation of upper bound and lower bound of entropy for 2D quantum systems.