Abstract
We consider as in [1] an infinite dynamical system idealized as aC*-algebra acted upon by time-translation automorphisms. We show that a stationary state of such a system which is stable for local perturbations of the dynamics and is clustering in time, either gives rise to a one-sided energy spectrum or is a KMS state. The clustering property assumed here is weaker than the one assumed in [1]. The new proof makes explicit use of spectral properties of clustering states.
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Communicated by J. L. Lebowitz
Supported by the Norwegian Research Council for Science and Humanities.
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Bratteli, O., Kastler, D. Relaxing the clustering condition in the derivation of the KMS property. Commun.Math. Phys. 46, 37–42 (1976). https://doi.org/10.1007/BF01610498
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DOI: https://doi.org/10.1007/BF01610498