Abstract
Let L be the Liouvillean of an ergodic quantum dynamical system (\(\mathfrak{M}\), τ, ω). We give a new proof of the theorem of Jadczyk that eigenvalues of L are simple and form a subgroup of \(\mathbb{R}\). If ω is a (τ, β)-KMS state for some β≠0 we show that this subgroup is trivial, namely that zero is the only eigenvalue of L. Hence, for KMS states ergodicity is equivalent to weak mixing.
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J. Dereziński, V. Jakšić, and C.-A. Pillet, in preparation.
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Jakšić, V., Pillet, CA. A Note on Eigenvalues of Liouvilleans. Journal of Statistical Physics 105, 937–941 (2001). https://doi.org/10.1023/A:1013561529682
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DOI: https://doi.org/10.1023/A:1013561529682