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Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells II. (English) Zbl 1157.82046

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.

MSC:

82D37 Statistical mechanics of semiconductors
35Q55 NLS equations (nonlinear Schrödinger equations)
34L25 Scattering theory, inverse scattering involving ordinary differential operators
34L30 Nonlinear ordinary differential operators
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65Z05 Applications to the sciences
81Q20 Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory
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