[Quasicristaux, ordre apériodique, et algèbres von Neumann]
On introduit des opérateurs « tight binding » pour des quasicristaux paramétrés par des ensembles de Delone. On peut regarder ces opérateurs dans le contexte naturel des algèbres de von Neumann. Un tel point de vue permet d'étudier la théorie spectrale. En particulier la densité d'états intégrée est liée à une trace de l'algèbre.
We introduce tight binding operators for quasicrystals that are parametrized by Delone sets. These operators can be regarded in a natural operator algebra framework that encodes the long range aperiodic order. This algebraic point of view allows us to study spectral theoretic properties. In particular, the integrated density of states of the tight binding operators is related to a canonical trace on the associated von Neumann algebra.
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Daniel Lenz 1 ; Peter Stollmann 1
@article{CRMATH_2002__334_12_1131_0,
author = {Daniel Lenz and Peter Stollmann},
title = {Quasicrystals, aperiodic order, and groupoid von {Neumann} algebras},
journal = {Comptes Rendus. Math\'ematique},
pages = {1131--1136},
publisher = {Elsevier},
volume = {334},
number = {12},
year = {2002},
doi = {10.1016/S1631-073X(02)02401-9},
language = {en},
}
Daniel Lenz; Peter Stollmann. Quasicrystals, aperiodic order, and groupoid von Neumann algebras. Comptes Rendus. Mathématique, Volume 334 (2002) no. 12, pp. 1131-1136. doi : 10.1016/S1631-073X(02)02401-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02401-9/
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