1 citations · 1 across the 3 of their papers we have counts for
6 papers
The Dry Ten Martini Problem for Sturmian Hamiltonians
Ram Band, Siegfried Beckus, Raphael Loewy
The dry ten Martini problem for Sturmian Hamiltonians is solved. Concretely, we prove that all the predicted spectral gaps "are there" for all the Schrödinger operators with Sturm…
Complete hierarchical structure of the spectral bands in the Kohmoto model
Ram Band, Siegfried Beckus, Raphael Loewy
We study the Kohmoto model, a family of discrete Schrödinger operators with Sturmian potentials depending on a frequency and a coupling constant. We prove that, for all non-vanish…
Spectral pollution in substitution systems
Ram Band, Siegfried Beckus, Felix Pogorzelski +1
We study spectral properties of Schrödinger operators associated with substitution dynamical systems in higher dimensions. Focusing on periodic approximations generated by iterati…
From Quasiperiodicity to a Complete Coloring of the Kohmoto Butterfly
Ram Band, Siegfried Beckus
The spectra of the Kohmoto model give rise to a fractal phase diagram, known as the Kohmoto butterfly. The butterfly encapsulates the spectra of all periodic Kohmoto Hamiltonians,…
Spectral approximation for substitution systems
Ram Band, Siegfried Beckus, Felix Pogorzelski +1
We study periodic approximations of aperiodic Schrödinger operators on lattices in Lie groups with dilation structure. The potentials arise through symbolic substitution systems t…
A review of a work by Raymond: Sturmian Hamiltonians with a large coupling constant -- periodic approximations and gap labels
Ram Band, Siegfried Beckus, Barak Biber +2
We present a review of the work L. Raymond from 1995. The review aims at making this work more accessible and offers adaptations of some statements and proofs. In addition, this re…