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Pré-Publication, Document De Travail Année : 2007

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

Résumé

We describe the asymptotic of the steady states of the out-of equilibrium Schrödinger-Poisson system, in the regime of quantum wells in a semiclassical island. After establishing uniform estimates on the nonlinearity, we show that the nonlinear steady states lie asymptotically in a finite-dimensional subspace of functions and that the involved spectral quantities are reduced to a finite number of so-called asymptotic resonant energies. The asymptotic finite dimensional nonlinear system is written in a general setting with only a partial information on its coefficients. After this first part, a complete derivation of the asymptotic nonlinear system will be done for some specific cases in a forthcoming article. UNE VERSION MODIFIEE DE CE TEXTE EST PARUE DANS LES ANNALES DE L'INSTITUT H. POINCARE, ANALYSE NON LINEAIRE.
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Dates et versions

hal-00124683 , version 1 (15-01-2007)

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  • HAL Id : hal-00124683 , version 1

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Virginie Bonnaillie-Noël, Francis Nier, Mamodyasine Patel. Far from equilibrium steady states of 1D-Schrödinger-Poisson systems with quantum wells I. 2007. ⟨hal-00124683⟩
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