Noncommutative space and the low-energy physics of quasicrystals
  We prove that the effective low-energy, nonlinear Schroedinger equation for a particle in the presence of a quasiperiodic potential is the potential-free, nonlinear Schroedinger equation on noncommutative space. Thus quasiperiodicity of the potential can be traded for space noncommutativity when describing the envelope wave of the initial quasiperiodic wave. 
L. Monreal, P. Fernandez de Cordoba, A. Ferrando, J. M. Isidro