Global controllability of the 1D Schrödinger–Poisson equation

Mariano De Leo ^[1] ; Constanza Sánchez Fernández de la Veg ^[2] ; Diego Rial ^[2]
1. [1] Universidad Nacional de General Sarmiento
  
  Universidad Nacional de General Sarmiento
  
  Argentina
2. [2] Universidad de Buenos Aires
  
  Universidad de Buenos Aires
  
  Argentina
Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 54, Nº. 1, 2013, págs. 43-54
Idioma: inglés
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Resumen
- This paper is concerned with both the local and global internal controllability of the 1D Schrödinger–Poisson equation iut(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 profile 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.