Inflow boundary conditions for the time dependent one-dimensional Schrodinger equation

Authors
Ben Abdallah, N Degond, P Gamba, I
Citation
N. Ben Abdallah et al., Inflow boundary conditions for the time dependent one-dimensional Schrodinger equation, CR AC S I, 331(12), 2000, pp. 1023-1028
Citations number
9
Categorie Soggetti
Mathematics
Journal title
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE
ISSN journal
07644442 → ACNP
Volume
331
Issue
12
Year of publication
2000
Pages
1023 - 1028
Database
ISI
SICI code
0764-4442(200012)331:12<1023:IBCFTT>2.0.ZU;2-2
Abstract
A transient quantum model fur one-dimensional charge transport is derived a nd shown to lead in the semiclassical limit to the Vlasov equation with inf low boundary conditions. Asymptotic formulae involving quantum reflection-t ransmission coefficients and time delays are used to construct a hybrid mod el coupling quantum descriptions to kinetic ones in a time-dependent one-di mensional setting. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.