Global controllability of 1D Schroedinger-Poisson equation

This paper is concerned with both the local and global internal controllability of the 1D Schroedinger-Poisson equation i u_t =  -u_xx +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 incl...

Descripción completa

Detalles Bibliográficos
Autores: de Leo, Mariano Fernando, Sanchez Fernandez de la Vega, Constanza Mariel, Rial, Diego Fernando
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2013
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/10689
Acceso en línea:http://hdl.handle.net/11336/10689
Access Level:acceso abierto
Palabra clave:Nonlinear Schroedinger-Poisson
Hartree potential
doping profile
internal controllability
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:This paper is concerned with both the local and global internal controllability of the 1D Schroedinger-Poisson equation i u_t =  -u_xx +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 prole 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.