Abstract: This chapter discusses the physical properties of aperiodic crystals. Topics covered include tensorial properties, hydrodynamics, phonons, phasons, non-linear excitations, and electrons. It is shown that phonons and electrons in quasiperiodic crystals behave differently from those in periodic crystals. The most important differences include: (i) phonon eigenvectors and electron states occur as extended, as found in all periodic crystals, but they also occur as localized or as critical; (ii) quasiperiodic crystals show examples of absolute continuous, singular continuous, and point parts in their spectra; and (iii) electron and phonon dispersion curves have an infinite number of gaps, although these may be negligible for modulated phases and composites.

Keywords: aperiodic crystals, tensorial properties, hydrodynamics, phonons, phasons, non-linear excitations, electrons,