Abstract:
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. |