Abstract:
We develop semiclassical models and multiscale computational methods for
quantum dynamics with non-adiabatic effects. Applications of such methods
include surface hopping, Schrodinger equation with periodic potentials,
elastic and electromagnetic waves with polarizations, and graphene. We use
the Wigner transform to derive these models. The key idea is to evolve the
dynamics of the entire Wigner matrices, which contain important non-adiabatic terms,
not just the diagonal projections corresponding to the eigenstates of the Hamiltonians. We also develop multiscale computational methods based on these models and numerical examples will be used to show the validity of these models in captuing the quantum transitions at the crossing-points. |