  Deterministically aperiodic sequences are an intermediary between periodic
sequences and completely random sequences. Materials which are translationally
periodic have Bloch-like extended states, while random media exhibit Anderson
localisation. Materials constructed on the basis of deterministic aperiodic
sequences such as Fibonacci, Thue-Morse, and Rudin-Shapiro exhibit different
properties, which can be related to their spectrum. Here, by investigating the
dynamics of discrete-time quantum walks using different aperiodic sequences of
coin operations in position space and time we establish the role of the
diffraction spectra in characterizing the spreading of the wavepacket.

Quantum Physics;Disordered Systems and Neural Networks