Darboux Transformations of Bispectral Quantum Integrable Systems
Horozov, Emil ; Kasman, Alex
arXiv, 9806002 / Harvested from arXiv
Text on arXiv
We present an approach to higher dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differential operators. Specifically, working with the algebro-geometric definition of quantum integrability, we utilize the bispectral duality of quantum Hamiltonian systems to construct non-trivial Darboux transformations between completely integrable quantum systems. As an application, we are able to construct new quantum integrable systems as the Darboux transforms of trivial examples (such as symmetric products of one dimensional systems) or by Darboux transformation of well-known bispectral systems such as quantum Calogero-Moser.
Publié le : 1998-06-05
Classification:  Mathematical Physics,  Mathematics - Commutative Algebra,  Nonlinear Sciences - Exactly Solvable and Integrable Systems,  Quantum Physics,  81S05 13N10 58G37 58F07 47F05 32C38 
@article{9806002,
     author = {Horozov, Emil and Kasman, Alex},
     title = {Darboux Transformations of Bispectral Quantum Integrable Systems},
     journal = {arXiv},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9806002}
}

Horozov, Emil; Kasman, Alex. Darboux Transformations of Bispectral Quantum Integrable Systems. arXiv, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/9806002/