|
|
| |
| A SCATTERING MATRIX MODEL OF SEMICONDUCTOR SUPERLATTICES IN MULTIDIMENSIONALWAVE-VECTOR SPACE AND ITS DIFFUSION LIMIT |
| |
Citation： |
P. Degond,ZHANG Kaijun.A SCATTERING MATRIX MODEL OF SEMICONDUCTOR SUPERLATTICES IN MULTIDIMENSIONALWAVE-VECTOR SPACE AND ITS DIFFUSION LIMIT[J].Chinese Annals of Mathematics B,2003,24(2):167~190 |
| Page view： 1427
Net amount： 808 |
Authors： |
P. Degond; ZHANG Kaijun |
Foundation： |
Project supported by the TMR network No. ERB FMBX CT97 0157 on ‘Asymptotic methods in
kinetic theory’ of the European Community, the LIAMA (Laboratoire d’Informatique, Automatique
et Mathematiques Appliquees), the PRA (Programme de Recherches Avancees), by the Austrian
Start prize “Nonlinear Schrodinger Equations and Quantum Boltzmann Equations”(Y-137-TEC) and
by the National Natural Science Foundation of China (No. 10271003). |
|
|
| Abstract： |
The authors first establish a quantum microscopic scattering matrix model
in multidimensional wave-vector space, which relates the phase
space density of each superlattice cell with that of the
neighbouring cells. Then, in the limit of a large number of cells,
a SHE (Spherical Harmonics Expansion)-type model of diffusion
equations for the particle number density in the position-energy
space is obtained. The crucial features of diffusion constants on
retaining the memory of the quantum scattering characteristics of
the superlattice elementary cell (like e.g. transmission
resonances) are shown in order. Two examples are treated with the
analytically computation of the diffusion constants. |
Keywords： |
Superlattices, Scattering matrix model, Diffusion approximation,
Spherical harmonics expansion, Drift-diffusion, Energy transport,
Transmission resonance |
Classification： |
35Q20, 76P05, 82A70, 78A35 |
|
|
Download PDF Full-Text
|
|
|
|
