Smilansky's model of irreversible quantum graphs, I: the absolutely continuous spectrum
Evans, W. D. ; Solomyak, M.
arXiv, 0503497 / Harvested from arXiv
Text on arXiv
In the model suggested by Smilansky one studies an operator describing the interaction between a quantum graph and a system of $K$ one-dimensional oscillators attached at several different points in the graph. The present paper is the first one in which the case $K>1$ is investigated. For the sake of simplicity we consider K=2, but our argument is of a general character. In this first of two papers on the problem, we describe the absolutely continuous spectrum. Our approach is based upon scattering theory.
Publié le : 2005-03-23
Classification:  Mathematics - Spectral Theory,  Mathematical Physics,  81Q10,  81Q15 
@article{0503497,
     author = {Evans, W. D. and Solomyak, M.},
     title = {Smilansky's model of irreversible quantum graphs, I: the absolutely
  continuous spectrum},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0503497}
}

Evans, W. D.; Solomyak, M. Smilansky's model of irreversible quantum graphs, I: the absolutely
  continuous spectrum. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0503497/