Delone dynamical systems and associated random operators

Details Delone dynamical systems and associated random operators Delone dynamical systems and associated random operators

2002-02-26

arxiv.org/abs/math-ph/0202042v2

Physics

Mathematical Physics

19 pages; revised version

Scientific paper

We carry out a careful study of basic topological and ergodic features of Delone dynamical systems. We then investigate the associated topological groupoids and in particular their representations on certain direct integrals with non constant fibres. Via non-commutative-integration theory these representations give rise to von Neumann algebras of random operators. Features of these algebras and operators are discussed. Restricting our attention to a certain subalgebra of tight binding operators, we then discuss a Shubin trace formula.

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