3 papers
math-ph2026
Bottleneck Effects and Harmonic-Type Velocity Bounds for Periodic Quantum Walks
Houssam Abdul-Rahman, Thomas A. Jackson, Darren C. Ong
We prove explicit upper bounds on the propagation velocity of one-dimensional quantum walks with periodic coins of arbitrary period. We treat two complementary settings. First, in…
math.CO2025
Average Degree of Graphs Derived From The Ammann A2 Aperiodic Tiling
Xinyan Xu, Darren C. Ong
The Ammann A2 tiling is a simple aperiodically ordered tiling of the plane. We consider the graph derived from this tiling, by treating each corner of each tile as a vertex and eac…
math.DS2024
Fractals corresponding to the metallic means sequences
Y. S. J. Liang, Darren C. Ong
In this work, we introduce a class of fractal subsets of corresponding to the aperiodically ordered metallic means sequences. We find simple formulas for the fractal dimens…