Mathematical and Computational Methods in Quantum Chemistry

Semiclassical computational methods for quantum dynamics with band-crossing

Shi Jin

University of Wisconsin-Madison

Band-crossing is a quantum dynamical behavior that contributes to important physics and chemistry phenomena such as quantum tunneling, Berry c onnection, chemical reaction etc. In this talk, we will discuss several recent works in developing semiclassical methods for band-crossing, including examples from surface hopping, Schrodinger equation with periodic potentials, and high frequency solutions of linear hyperbolic systems with polarized waves. For such systems we will also introduce an "asymptotic-preserving" method that is accurate uniformly for all wave numbers.