States of a one dimensional quantum crystal

Amour, Laurent; Cancelier, Claudy; Levy-Bruhl, Pierre; Nourrigat, Jean

Comptes Rendus. Mathématique, Tome 336 (2003) no. 12, pp. 981-984.

Nous construisons des états d'équilibre sur une C^★ algèbre associée à un cristal quantique unidimensionnel. Nous étudions la valeur moyenne d'une observable, non nécessairement bornée, telle que le coefficient de dilatation. Ceci demande, d'une part, une analyse précise du noyau de la chaleur associé au cristal et, d'autre part, l'étude des corrélations quantiques de deux observables associés a deux amas de particules.

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 particules.

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