Doi: http://dx.doi.org/10.15446/recolma.v49n1.54167
1Universidad Sergio Arboleda, Bogotá, Colombia. Email: leonardo.cano@usa.edu.co
We show the existence and orthogonality of wave operators naturally associated to a compatible Laplacian on a complete manifold with a corner of codimension 2. In fact, we prove asymptotic completeness i.e. that the image of these wave operators is equal to the space of absolutely continuous states of the compatible Laplacian. We achieve this last result using time dependent methods coming from many-body Schrödinger equations.
Key words: Quantum scattering theory, Manifolds with corners, Wave operators, Many-body Schrödinger equations.
Demostramos la existencia y ortogonalidad de operadores de onda naturalmente asociados a un Laplaciano compatible sobre una variedad completa con una esquina de codimensión 2. De hecho, probamos su completitud asintótica, es decir que la imagen de esos operadores de onda es igual al espacio de estados absolutamente contínuos del Laplaciano compatible. Logramos esto último usando métodos dependientes del tiempo que provienen del estudio de operadores de Schrödinger de varios cuerpos.
Palabras clave: Teoría de dispersión cuántica, variedades con esquinas, operadores de onda, ecuaciones de Schrödinger de varios cuerpos.
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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
Doi: http://dx.doi.org/ @ARTICLE{RCMv49n1a06,
AUTHOR = {Cano G., Leonardo A.},
TITLE = {{Time Dependent Quantum Scattering Theory on Complete Manifolds with a Corner of Codimension 2}},
JOURNAL = {Revista Colombiana de Matemáticas},
YEAR = {2015},
volume = {49},
number = {1}, ]]>
pages = {105--138}
}