29 citations · 64 across the 12 of their papers we have counts for
17 papers
The butterflies' effects
Siegfried Beckus
This work studies spectral properties of Schrödinger operators in the context of aperiodic order, using weighted Delone sets to explore the interplay between the underlying dynamic…
Spectral regularity and defects for the Kohmoto model
Siegfried Beckus, Jean Bellissard, Yannik Thomas
We study the Kohmoto model including Sturmian Hamiltonians and the associated Kohmoto butterfly. We prove spectral estimates for the operators using Farey numbers. In addition, we…
Spectral estimates of dynamically-defined and amenable operator families
Siegfried Beckus, Alberto Takase
We consider kernel operators defined by a dynamical system. The Hausdorff distance of spectra is estimated by the Hausdorff distance of subsystems. We prove that the spectrum map i…
Symbolic substitution systems beyond abelian groups
Siegfried Beckus, Tobias Hartnick, Felix Pogorzelski
In this article we construct the first examples of strongly aperiodic linearly repetitive Delone sets in non-abelian Lie groups by means of symbolic substitutions. In particular, w…
Growth of Eigenfunctions and R-limits on Graphs
Siegfried Beckus, Latif Eliaz
A characterization of the essential spectrum of Schrödinger operators on infinite graphs is derived involving the concept of -limits. This concept, whi…
Linear repetitivity beyond abelian groups
Siegfried Beckus, Tobias Hartnick, Felix Pogorzelski
We show that linearly repetitive weighted Delone sets in groups of polynomial growth have a uniquely ergodic hull. This result applies in particular to the linearly repetitive weig…
Generalized eigenfunctions and eigenvalues: a unifying framework for Shnol-type theorems
Siegfried Beckus, Baptiste Devyver
Let be a generalized Schrödinger operator on a domain of a non-compact connected Riemannian manifold, and a generalized eigenfunction for : that is, satisfies the eq…
Hölder Continuity of the Spectra for Aperiodic Hamiltonians
Siegfried Beckus, Jean Bellissard, Horia Cornean
We study the spectral location of strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to…
Spectral Continuity for Aperiodic Quantum Systems II. Periodic Approximations in 1D
Siegfried Beckus, Jean Bellissard, Giuseppe De Nittis
The existence and construction of periodic approximations with convergent spectra is crucial in solid state physics for the spectral study of corresponding Schrödinger operators. I…
Delone dynamical systems and spectral convergence
Siegfried Beckus, Felix Pogorzelski
In the realm of Delone sets in locally compact, second countable, Hausdorff groups, we develop a dynamical systems approach in order to study the continuity behavior of measured qu…
Spectral Continuity for Aperiodic Quantum Systems I. General Theory
Siegfried Beckus, Jean Bellissard, Giuseppe De Nittis
How does the spectrum of a Schrödinger operator vary if the corresponding geometry and dynamics change? Is it possible to define approximations of the spectrum of such operators by…
Shnol-type theorem for the Agmon ground state
Siegfried Beckus, Yehuda Pinchover
Let be a Schrödinger operator defined on a noncompact Riemannian manifold , and let . Suppose that the operator is critical in , and le…
Spectral approximation of aperiodic Schrödinger operators
Siegfried Beckus
We study the (Hölder-)continuous behavior of the spectra belonging to a family of linear bounded operators indexed by a topological space . For the cases of sel…
On the spectrum of operator families on discrete groups over minimal dynamical systems
Siegfried Beckus, Daniel Lenz, Marko Lindner +1
It is well known that, given an equivariant and continuous (in a suitable sense) family of selfadjoint operators in a Hilbert space over a minimal dynamical system, the spectrum of…
Continuity of the spectrum of a field of self-adjoint operators
Siegfried Beckus, Jean Bellissard
Given a family of self-adjoint operators indexed by a parameter in some topological space , necessary and sufficient conditions are given for the spectrum $…
Note on spectra of non-selfadjoint operators over dynamical systems
Siegfried Beckus, Daniel Lenz, Marko Lindner +1
We consider equivariant continuous families of discrete one-dimensional operators over arbitrary dynamical systems. We introduce the concept of a pseudo-ergodic element of a dynami…
Spectrum of Lebesgue measure zero for Jacobi matrices of quasicrystals
Siegfried Beckus, Felix Pogorzelski
We study one-dimensional random Jacobi operators corresponding to strictly ergodic dynamical systems. In this context, we characterize the spectrum of these operators by non-unifor…