Mathematical and Numerical Methods for Complex Quantum Systems

Computing high frequency solutions of symmetric hyperbolic systems with polarized waves

Leland Jefferis

University of Wisconsin - Madison

We develop a method for computing the Gaussian beam solution for a general class of symmetric hyperbolic systems in both Lagrangian and Eulerian frames. Symmetric hyperbolic systems include many physically relevant systems of partial differential equations (PDE) such as Maxwell's equations, the elastic equations and the acoustic equations. We extend the Gaussian beam method to the regime of symmetric hyperbolic systems with constant degeneracy. Finally I will discuss the interesting potential for this method to handle non-constant degeneracy and eigenvalue crossing points in the hyperbolic systems and Schrödinger equation cases.