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Stability And Equilibrium States

Rudolf Haag, Daniel Kastler, Ewa B. Trych-Pohlmeyer
Published 1974 · Mathematics
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For an infinite dynamical quantum system idealized as aC*-algebra acted upon by time-translations automorphisms in an asymptotically abelian way, we propose to characterize equilibrium states by the three properties of stationarity, stability for local perturbations of the dynamics, and relative purity. We show that a state with these properties either gives rise to a one-sided energy spectrum or is a KMS- (i.e. essentially a limit Gibbs-) state.



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