摘要
The authors first establish a quantum microscopic scattering matrix model in multidimen-sional wave-vector space, which relates the phase space density of each superlattice cell withthat of the neighbouring cells. Then, in the limit of a large number of cells, a SHE (SphericalHarmonics Expansion)-type model of diffusion equations for the particle number density in theposition-energy space is obtained. The crucial features of diffusion constants on retaining thememory 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 analyticallycomputation of the diffusion constants.
基金
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),the Aust
