Electrons in deterministic quasicrystalline potentials and hidden conserved quantities

P Kalugin, A Katz - Journal of Physics A: Mathematical and …, 2014 - iopscience.iop.org
We propose an ansatz for the wave function of a non-interacting quantum particle in a
deterministic quasicrystalline potential. It is applicable to both continuous and discrete …

Self affine Delone sets and deviation phenomena

S Schmieding, R Trevino - Communications in Mathematical Physics, 2018 - Springer
We study the growth of norms of ergodic integrals for the translation action on spaces
coming from expansive, self-affine Delone sets. The linear map giving the self-affinity …

[PDF][PDF] Pure discrete spectrum in substitution tiling spaces

M Barge, S Štimac, RF Williams - arxiv preprint arxiv:1107.3598, 2011 - arxiv.org
arxiv:1107.3598v1 [math.DS] 19 Jul 2011 Page 1 arxiv:1107.3598v1 [math.DS] 19 Jul 2011
PURE DISCRETE SPECTRUM IN SUBSTITUTION TILING SPACES M. BARGE, S. ŠTIMAC …

Conjugacies of model sets

J Kellendonk, L Sadun - arxiv preprint arxiv:1406.3851, 2014 - arxiv.org
Let $ M $ be a model set meeting two simple conditions:(1) the internal space $ H $ is a
product of $ R^ n $ and a finite group, and (2) the window $ W $ is a finite union of disjoint …

The Cech cohomology and the spectrum for 1-dimensional tiling systems

TI Andress, EA Robinson Jr - … the continuing influence of John C …, 2016 - books.google.com
This paper discusses the relation between three groups: the dynamical cohomology H (T) of
a substitution shift dynamical system T, the first integer Cech cohomology group ˇH1 (Y) of …

Bragg spectrum, K-theory, and gap labeling of aperiodic solids

J Kellendonk - Journal of Mathematical Physics, 2023 - pubs.aip.org
The diffraction spectrum of an aperiodic solid is related to the group of eigenvalues of the
dynamical system associated with the solid. Those eigenvalues with continuous …

Aperiodicity, rotational tiling spaces and topological space groups

J Hunton, JJ Walton - Advances in Mathematics, 2021 - Elsevier
We study the rotational structures of aperiodic tilings in Euclidean space of arbitrary
dimension using topological methods. Classical topological approaches to the study of …

Model sets with Euclidean internal space

MA Cerda, D Coronel - Ergodic Theory and Dynamical Systems, 2023 - cambridge.org
We give a characterization of inter-model sets with Euclidean internal space. This
characterization is similar to previous results for general inter-model sets obtained …

Continuous eigenvalues for repetitive Meyer systems

M Allendes Cerda - 2021 - repositorio.uchile.cl
Esta tesis doctoral realiza una contribución al estudio de valores propios para sistemas
dinámicos asociados a algunos conjuntos discretos y repetitivos en R d: Delone, Meyer …

Simple dimension groups that are isomorphic to stationary inductive limits

G Maloney - Transactions of the American Mathematical Society, 2023 - ams.org
A dimension group is an ordered abelian group that is an inductive limit of a sequence of
simplicial groups, and a stationary dimension group is such an inductive limit in which the …