Generalized Thue-Morse chains and their physical properties

We study the physical properties of the Thue-Morse chain and its generalizations. After a preliminary discussion of its basic features (e.g., structure factor, location, and relative magnitude of spectral gaps), we focus on (1) the trace maps of generalized Thue-Morse lattices, (2) a detailed analysis of the attractor of the associated dynamical system, (3) the electronic spectra through the trace-map approach, (4) spin excitations in a quantum Ising model in a transverse magnetic field, (5) light transmission through a multilayer, and (6) the diamagnetic properties of Thue-Morse superconducting wire networks and Josephson-junction arrays.