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Nonlinear von Neumann-type equations: Darboux invariance and spectra

Maciej Kuna·Marek Czachor·Sergiej B. Leble
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Abstract

Generalized Euler-Arnold-von Neumann density matrix equations can be solved by a binary Darboux transformation given here in a new form: $\rho[1]=e^{P\ln(\mu/\nu)}\rho e^{-P\ln(\mu/\nu)}$ where $P=P^2$ is explicitly constructed in terms of conjugated Lax pairs, and $\mu$, $\nu$ are complex. As a result spectra of $\rho$ and $\rho[1]$ are identical. Transformations allowing to shift and rescale spectrum of a solution are introduced, and a class of stationary seed solutions is discussed.

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Maciej Kuna, Marek Czachor, Sergiej B. Leble. 1998-10-07. Nonlinear von Neumann-type equations: Darboux invariance and spectra. https://doi.org/10.1016/s0375-9601(99)00157-7

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