The spectrum of the Liouville–von Neumann operator

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Abstract
We relate the pure point spectrum, the singularly continuous, and the absolutely continuous part of the spectrum of the Liouville–von Neumann operator [H,⋅] to the respective parts of the spectrum of the Hamiltonian operator H. As a consequence of this result we obtain a theorem about the weak* limit of the time evolution W (t) of a normal state W for t → ∞.

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