Global controllability of the 1D schrödinger-poisson equation

This paper is concerned with both the local and global internal controllability of the 1D Schrödinger-Poisson equation i ut(x, t) = -uxx + V (u) u; which arises in quantum semiconductor models. Here V (u) is a Hartree-type nonlinearity stemming from the coupling with the 1D Poisson equation, which i...

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Autores principales: De Leo, Mariano Fernando, Rial, Diego Fernando
Publicado: 2013
Materias:
Doping prole
Hartree potential
Internal controllability
Nonlinear Schrödinger-Poisson
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v54_n1_p43_Deleo
http://hdl.handle.net/20.500.12110/paper_00416932_v54_n1_p43_Deleo
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00416932_v54_n1_p43_Deleo
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spelling paper:paper_00416932_v54_n1_p43_Deleo2025-07-30T17:45:19Z Global controllability of the 1D schrödinger-poisson equation De Leo, Mariano Fernando Rial, Diego Fernando Doping prole Hartree potential Internal controllability Nonlinear Schrödinger-Poisson This paper is concerned with both the local and global internal controllability of the 1D Schrödinger-Poisson equation i ut(x, t) = -uxx + V (u) u; which arises in quantum semiconductor models. Here V (u) is a Hartree-type nonlinearity stemming from the coupling with the 1D Poisson equation, which includes the so-called doping prolle or impurities. More precisely, it is shown that for both attractive and repulsive self-consistent potentials depending on the balance between the total charge and the impurities this problem is globally internal controllable in a suitable Sobolev space. Fil:De leo, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rial, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2013 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v54_n1_p43_Deleo http://hdl.handle.net/20.500.12110/paper_00416932_v54_n1_p43_Deleo
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Doping prole
Hartree potential
Internal controllability
Nonlinear Schrödinger-Poisson
spellingShingle Doping prole
Hartree potential
Internal controllability
Nonlinear Schrödinger-Poisson
De Leo, Mariano Fernando
Rial, Diego Fernando
Global controllability of the 1D schrödinger-poisson equation
topic_facet Doping prole
Hartree potential
Internal controllability
Nonlinear Schrödinger-Poisson
description This paper is concerned with both the local and global internal controllability of the 1D Schrödinger-Poisson equation i ut(x, t) = -uxx + V (u) u; which arises in quantum semiconductor models. Here V (u) is a Hartree-type nonlinearity stemming from the coupling with the 1D Poisson equation, which includes the so-called doping prolle or impurities. More precisely, it is shown that for both attractive and repulsive self-consistent potentials depending on the balance between the total charge and the impurities this problem is globally internal controllable in a suitable Sobolev space.
author De Leo, Mariano Fernando
Rial, Diego Fernando
author_facet De Leo, Mariano Fernando
Rial, Diego Fernando
author_sort De Leo, Mariano Fernando
title Global controllability of the 1D schrödinger-poisson equation
title_short Global controllability of the 1D schrödinger-poisson equation
title_full Global controllability of the 1D schrödinger-poisson equation
title_fullStr Global controllability of the 1D schrödinger-poisson equation
title_full_unstemmed Global controllability of the 1D schrödinger-poisson equation
title_sort global controllability of the 1d schrödinger-poisson equation
publishDate 2013
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v54_n1_p43_Deleo
http://hdl.handle.net/20.500.12110/paper_00416932_v54_n1_p43_Deleo
work_keys_str_mv AT deleomarianofernando globalcontrollabilityofthe1dschrodingerpoissonequation
AT rialdiegofernando globalcontrollabilityofthe1dschrodingerpoissonequation
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