Multiphase semiclassical approximation of an electron in a one-dimensional crystalline lattice - III. From ab initio models to WKB for Schrödinger-Poisson

Authors:
Laurent Gosse;Norbert J. Mauser
Affiliations:
IAC-CNR "Mauro Picone" (sezione di Bari) Via G. Amendola 122/D, Bari 70126, Italy;Wolfgang Pauli Institute c/o Fak. f. Mathematik/ Univ. Wien Nordbergstrasse, 15, A-1090 Vienna, Austria
Venue:
Journal of Computational Physics
Year:
2006

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Abstract

This work is concerned with the semiclassical approximation of the Schrodinger-Poisson equation modeling ballistic transport in a 1D 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.