Propagation through Generic Level Crossings: A Surface Hopping Semigroup

Clotilde Fermanian Kammerer, Caroline Lasser
2008 SIAM Journal on Mathematical Analysis  
We construct a surface hopping semigroup, which asymptotically describes nuclear propagation through crossings of electron energy levels. The underlying time-dependent Schrödinger equation has a matrix-valued potential, whose eigenvalue surfaces have a generic intersection of codimension two, three or five in Hagedorn's classification. Using microlocal normal forms reminiscent of the Landau-Zener problem, we prove convergence to the true solution with an error of the order ε 1/8 , where ε is
more » ... semi-classical parameter. We present numerical experiments for an algorithmic realization of the semigroup illustrating the convergence of the algorithm.
doi:10.1137/070686810 fatcat:qi6pr2fczzdgti3n4fxd2rivhq