TY  - GEN
A1  - Beckus, Siegfried
A1  - Bellissard, Jean
A1  - De Nittis, Giuseppe
T1  - Corrigendum to:  Spectral continuity for aperiodic quantum systems I. General theory. - [Journal of functional analysis. - 275 (2018), 11, S. 2917 – 2977]
T2  - Journal of functional analysis
N2  - A correct statement of Theorem 4 in [1] is provided. The change does not affect the main results.
KW  - Haar system
Y1  - 2019
U6  - https://doi.org/10.1016/j.jfa.2019.06.001
SN  - 0022-1236
SN  - 1096-0783
VL  - 277
IS  - 9
SP  - 3351
EP  - 3353
PB  - Elsevier
CY  - San Diego
ER  - 
TY  - JOUR
A1  - Beckus, Siegfried
A1  - Bellissard, Jean
A1  - De Nittis, Giuseppe
T1  - Spectral continuity for aperiodic quantum systems
BT  - applications of a folklore theorem
JF  - Journal of mathematical physics
N2  - This work provides a necessary and sufficient condition for a symbolic dynamical system to admit a sequence of periodic approximations in the Hausdorff topology. The key result proved and applied here uses graphs that are called De Bruijn graphs, Rauzy graphs, or Anderson-Putnam complex, depending on the community. Combining this with a previous result, the present work justifies rigorously the accuracy and reliability of algorithmic methods used to compute numerically the spectra of a large class of self-adjoint operators. The so-called Hamiltonians describe the effective dynamic of a quantum particle in aperiodic media. No restrictions on the structure of these operators other than general regularity assumptions are imposed. In particular, nearest-neighbor correlation is not necessary. Examples for the Fibonacci and the Golay-Rudin-Shapiro sequences are explicitly provided illustrating this discussion. While the first sequence has been thoroughly studied by physicists and mathematicians alike, a shroud of mystery still surrounds the latter when it comes to spectral properties. In light of this, the present paper gives a new result here that might help uncovering a solution.
Y1  - 2020
U6  - https://doi.org/10.1063/5.0011488
SN  - 0022-2488
SN  - 1089-7658
VL  - 61
IS  - 12
PB  - American Institute of Physics
CY  - Melville, NY
ER  -