Time fractional evolution of two dipolar-coupled spins under DM and KSEA interactions

This research investigates the time-fractional dynamics of two interacting dipolar spins in the presence of the Dzyaloshinsky-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions, alongside a uniform external magnetic field. The main subject is to employ the time-fractional Schr & ouml;dinger equation in order to examine the time-fractional development of quantum resources within the dipolar spin system, initially prepared in either a separable or partially entangled state. The study employs the & ell;1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document} norm of coherence, logarithmic negativity, and local quantum uncertainty to evaluate quantum coherence, entanglement and nonclassical correlations, respectively. This examination encompasses various parameters including the fractional derivative order, initial state configurations, strengths of DM and KSEA interactions, and dipolar coupling. Our main findings reveal that these quantifiers increase over time and evolve towards states of maximal coherence, regardless of whether the system is initially in a separable or partially entangled state. Lower values of the fractional derivative parameter are observed to enhance or steady the memory of the produced fractional state, which demonstrates the significant influence of fractional time dynamics. Additionally, strong DM and KSEA interactions significantly enhance the levels of quantum correlations and coherence of the system, a trend mirrored by the dipolar coupling constants.