Quasicrystals and almost periodicity

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dc.creatorGouere, Jean-Baptiste
dc.date2002-12-03
dc.date.accessioned2026-07-07T04:29:37Z
dc.date.available2026-07-07T04:29:37Z
dc.descriptionWe introduce a topology ${\cal T}$ on the space $U$ of uniformly discrete subsets of the Euclidean space. Assume that $S$ in $U$ admits a unique autocorrelation measure. The diffraction measure of $S$ is purely atomic if and only if $S$ is almost periodic in $(U,{\cal T})$. This result relates idealized quasicrystals to almost periodicity. In the context of ergodic point processes, the autocorrelation measure is known to exist. Then, the diffraction measure is purely atomic if and only if the dynamical system has a pure point spectrum. As an illustration, we study deformed model sets.
dc.identifierhttps://arxiv.org/abs/math-ph/0212012
dc.identifierhttp://arxiv.org/abs/math-ph/0212012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57228
dc.subjectMathematical Physics
dc.subjectProbability
dc.subject52C23; 60G55
dc.titleQuasicrystals and almost periodicity
dc.typetext

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