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Equivalence of various characterizations of equilibrium states for quantum lattice systems of spins and Fermions.
Probability| Speaker: | Huzihiro Araki, UC Davis and RIMS, Kyoto University |
| Location: | 1147 MSB |
| Start time: | Tue, Oct 31 2006, 2:10PM |
C^*-dynamical systems are considered for quantum lattice systems of spins and Fermions. Equivalence of various characterizations of their equilibrium states is shown. Only under the assumption that all elements of the algebra based on any finite subset of the lattice has the first time derivative at time 0, the dynamics is shown to be associated with a unique standard potential (Colloquium talk) and, without any further assumption, the above assertion is obtained. In particular, the implication of the KMS condition from the variational principle shown here solves a problem in the book of Bratteli and Robinson.