A study of the structure factor of Thue-Morse and period-doubling chains by wavelet analysis

One-dimensional systems generated by deterministic rules show interesting properties, such as a structure factor with peaks whose amplitudes scale with the size of the system according to a power law, with a scaling exponent in general dependent on the wavevector. I apply a wavelet transform to the structure factor of the Thue-Morse and the period-doubling chains and show how this technique succeeds in computing the scaling exponents and in finding the wavevector associated with them. This example shows that wavelet analysis could become an efficient tool for studying the Fourier transform of aperiodic systems.