Lie algebras for time evolution with applications from chaos studies to spintronics

POSTER

Abstract

We illustrate the power of Lie algebras in computing the time evolution of quantum systems with time-dependent physical parameters. By factorizing the quantum mechanical time evolution operator and using the linear independence of the Lie algebra generators, we reduce the operator equations to systems of coupled ordinary differential equations of scalar functions applicable to a variety of dynamical systems. We use the results to explore the possibility of detecting chaos in quantum nonlinear oscillators based on criteria from classical chaos studies and to follow spin currents in time-dependent spin-orbit coupled media.

Authors

  • Tim Wendler

    Brigham Young University

  • Manuel Berrondo

    Brigham Young University

  • Norm Buchanan

    Brigham Young University, Stanford University, University of Central Florida, NCAR/High Altitude Observatory, Arizona Vitro-retinal consultants, University of Michigan, Arizona State University, University of Denver, Arizona State University Dept of Physics, Arizona State University Dept of Chemistry and Biochemistry, LASP, University of Colorado Boulder, Center for Atmospheric and Space Science, Utah State University, Dixie State College, Utah, USU Materials Physics Group, UVU Physics Department, Box Elder Innovations, Space Telescope Science Institute, Northern Kentucky University, Retired, Utah Valley University, Univ. of California, Los Angelos, Colorado State University, St. Petersburg Electro-technical University, Universidad Nacional Aut\'onoma de M\'exico, New Mexico State University, University of New Mexico, University of Wurtzberg, Theoretical Division, Los Alamos National Laboratory, National High Magnetic Field Laboratory, LANL, UCLA, Max-planck-Institut f\"{u}r Astronomie, W. M. Keck Observatory, University of Arizona, Nuclear Physics Group, Brigham Young University, GLOBALFOUNDRIES, IBM Systems and Technology Group, IBM Research Division, T.J. Watson Research Center, Sandia National Laboratory, NMSU, Military University of Technology, Warsaw, Poland, James Franck Institute and Department of Physics, University of Chicago, Department of Atmospheric Sciences, University of Washington, JISAO, University of Washington, New Mexico Institute of Mining and Technology, NorthWest Research Associates, University of Alaska, Fairbanks, Utah State University, New Mexico Tech, University of Cambridge, Los Alamos National Laboratory, RAPTOR Science, Institute of Space and Astronomical Science, Japanese Aerospace Exploration Agency, Weber State University, Department of Physics, New Mexico State University, BYU Physics, Physics Department, University of Arizona, ABQMR, University of Colorado at Boulder, SNL and CINT, Los Alamos National Lab, Center for Quantum Information and Control, University of Arizona, Center for Quantum Information and Control, University of New Mexico, University of Calgary, Colorado School of Mines

  • Ryan T. Sayer

    Brigham Young University

  • Jean-Francois S. Van Huele

    Brigham Young University