Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice - III. From ab initio models to WKB for Schrodinger-Poisson
This work is concerned with the semiclassical approximation of the Schrodinger-Poisson equation modeling ballistic transport in a ID periodic potential by means of WKB techniques. It is derived by considering the mean-field limit of a N-body quantum problem, then K-multivalued solutions are adapted to the treatment of this weakly nonlinear system obtained after homogenization without taking into account for Pauli's exclusion principle. Numerical experiments display the behaviour of self-consistent wave packets and screening effects. (c) 2005 Elsevier Inc. All rights reserved.
periodic potential homogenization hartree ansatz semiclassical limit vlasov-poisson equation moment method nonstrictly hyperbolic systems