Journal of the Mathematical Society of Japan

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

Virginie BONNAILLIE-NOËL, Francis NIER, and Yassine PATEL

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Abstract

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.

Article information

Source
J. Math. Soc. Japan, Volume 61, Number 1 (2009), 65-106.

Dates
First available in Project Euclid: 9 February 2009

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1234189029

Digital Object Identifier
doi:10.2969/jmsj/06110065

Mathematical Reviews number (MathSciNet)
MR2272872

Zentralblatt MATH identifier
1157.82046

Subjects
Primary: 34L25: Scattering theory, inverse scattering 34L30: Nonlinear ordinary differential operators 34L40: Particular operators (Dirac, one-dimensional Schrödinger, etc.) 65L10: Boundary value problems 65Z05: Applications to physics 81Q20: Semiclassical techniques, including WKB and Maslov methods 82D37: Semiconductors

Keywords
Schrödinger-Poisson system asymptotic analysis multiscale problems

Citation

BONNAILLIE-NOËL, Virginie; NIER, Francis; PATEL, Yassine. Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells II. J. Math. Soc. Japan 61 (2009), no. 1, 65--106. doi:10.2969/jmsj/06110065. https://projecteuclid.org/euclid.jmsj/1234189029


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