NONCOMMUTATIVE SPACE AND THE LOW-ENERGY PHYSICS OF QUASICRYSTALS

We prove that the effective low-energy, nonlinear Schrödinger equation for a particle in the presence of a quasiperiodic potential is the potential-free, nonlinear Schrödinger 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.