Nonlinear von Neumann-type equations: Darboux invariance and spectra

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.

Phys.Lett.A - in print

References in corpus (2)

• Darboux-integrable nonlinear Liouville-von Neumann equation
• Microscopic Foundation of Nonextensive Statistics

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