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Special solutions of nonlinear von Neumann equations

Jan Naudts·Maciej Kuna
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Abstract

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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Jan Naudts, Maciej Kuna. 2006-02-12. Special solutions of nonlinear von Neumann equations. https://arxiv.org/abs/math-ph/0506020

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