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States of a one dimensional quantum crystal. (English) Zbl 1052.82004
Summary: We construct states on a \(C^*\)-algebra associated to a one-dimensional lattice crystal. We also compute the mean value of an observable, not necessarily bounded, such as the dilation coefficient. This implies on one hand, a careful analysis of the heat kernel of the Hamiltonian associated to the crystal and, on the other hand, the study of the quantum correlations of two observables associated to two clusters of particles.

MSC:
82B10 Quantum equilibrium statistical mechanics (general)
46L60 Applications of selfadjoint operator algebras to physics
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