Delone dynamical systems and associated random operators

2002/02/26 by Daniel Lenz, Lenz, Daniel, Peter Stollmann +1 · 1 citation
Mathematics · Physics and Astronomy · #52C23 #82B44 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:52C23 #msc:82B44

paper · pdf · doi:10.48550/arxiv.math-ph/0202042

19 pages; revised version

arxiv created 2002/05/13 · arxiv updated 2009/11/30

Abstract

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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