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

Journal Article · Sun Jan 01 00:00:00 EST 2006 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2005.05.020· OSTI ID:20687272

Gosse, Laurent ^[1]; Mauser, Norbert J ^[2]

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1. IAC-CNR 'Mauro Picone' (sezione di Bari) Via G. Amendola 122/D, Bari 70126 (Italy)
2. Wolfgang Pauli Institute c/o Fak. f. Mathematik, Univ. Wien Nordbergstrasse, 15, A-1090 Vienna (Austria)

This work is concerned with the semiclassical approximation of the Schroedinger-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.

• OSTI ID: 20687272
• Journal Information: Journal of Computational Physics, Vol. 211, Issue 1; Other Information: DOI: 10.1016/j.jcp.2005.05.020; PII: S0021-9991(05)00277-9; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CHARGED-PARTICLE TRANSPORT THEORY
CRYSTAL LATTICES
ELECTRONS
MATHEMATICAL SOLUTIONS
MEAN-FIELD THEORY
MOMENTS METHOD
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PAULI PRINCIPLE
PERIODICITY
POISSON EQUATION
POTENTIALS
SCHROEDINGER EQUATION
SEMICLASSICAL APPROXIMATION
SIMULATION
WAVE PACKETS
WKB APPROXIMATION