Special solutions of nonlinear von Neumann equations
Naudts, Jan ; Kuna, Maciej
arXiv, 0506020 / Harvested from arXiv
Text on arXiv
We consider solutions of the non-linear von Neumann equation involving Jacobi's elliptic functions sn, cn, and dn, and 3 linearly independent operators. In two cases one can construct a state-dependent Hamiltonian which is such that the corresponding non-linear von Neumann equation is solved by the given density operator. We prove that in a certain context these two cases are the only possibilities to obtain special solutions of this kind. Well-known solutions of the reduced Maxwell-Bloch equations produce examples of each of the two cases. Also known solutions of the non-linear von Neumann equation in dimension 3 are reproduced by the present approach.
Publié le : 2005-06-09
Classification:  Mathematical Physics,  35Q55 
@article{0506020,
     author = {Naudts, Jan and Kuna, Maciej},
     title = {Special solutions of nonlinear von Neumann equations},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0506020}
}

Naudts, Jan; Kuna, Maciej. Special solutions of nonlinear von Neumann equations. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0506020/