Special solutions of nonlinear von Neumann equations

Details Special solutions of nonlinear von Neumann equations Special solutions of nonlinear von Neumann equations

2005-06-09

arxiv.org/abs/math-ph/0506020v2

Physics

Mathematical Physics

extended from 13 to 21 pages (extra example, two theorems added)

Scientific paper

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.

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