Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells II

This article continues the asymptotic analysis of a nonlinear Schrödinger-Poisson system which models in a far from equilibrium regime the quantum transport in electronic devices like resonant tunneling diodes. Within the reduction to an h -dependent linear problem with uniform regularity estimates...

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Bibliographic Details
Published in:Journal of the Mathematical Society of Japan 2009-01, Vol.61 (1), p.65-106
Main Authors: BONNAILLIE-NOËL, Virginie, NIER, Francis, PATEL, Yassine
Format: Article
Language:English
Subjects:
34L25
34L30
34L40
65L10
65Z05
81Q20
82D37
asymptotic analysis
multiscale problems
Schrödinger-Poisson system
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Summary:This article continues the asymptotic analysis of a nonlinear Schrödinger-Poisson system which models in a far from equilibrium regime the quantum transport in electronic devices like resonant tunneling diodes. Within the reduction to an h -dependent linear problem with uniform regularity estimates for the potential already established in the first part, explicit computations of the asymptotic finite dimensional nonlinear system are derived. They rely on an accurate (phase-space) analysis of the tunnel effect which relies on some kind of Breit-Wigner formula and Fermi golden rule.
ISSN:0025-5645
1881-2333
DOI:10.2969/jmsj/06110065