Formation of Information Entropy in Spinor Bose-Einstein Condensates

In this paper, we investigate the information entropy formation in a spinor (F = 1) Bose-Einstein condensates (BECs) by numerically solving the three-dimensional Gross-Pitaevskii equation (GPE). The effect of the spin-independent interaction c0′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${c}_{0}^{\prime }$\end{document}, spin-dependent interaction c2′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${c}_{2}^{\prime }$\end{document} and external magnetic field Bext is discussed. We reveal that the position component Sr and total entropy S increase and the momentum component Sk decreases with increasing the c0′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${c}_{0}^{\prime }$\end{document} or Bext. Moreover, the order parameter δ decreases with increasing c0′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${c}_{0}^{\prime }$\end{document} or Bext, implying that the system becomes a more disordered state. However, for the side of c2′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${c}_{2}^{\prime }$\end{document}, we find that the information entropy keep almost constant irrespective of c2′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${c}_{2}^{\prime }$\end{document}, and the extent of disorder is also invariability.