The wave localization landscape
In disordered systems or systems with complex geometry, standing waves can obey a phenomenon called “localization”. This localization consists in a concentration of the wave energy in a very restricted sub-region of the whole domain, and can occur even in the absence of any classical confinement. It has been observed experimentally in mechanics, acoustics and quantum physics. In this talk, I will present a theory that reveals an underlying and universal structure, the “localization landscape”, which is the solution of a Dirichlet problem associated to the wave equation. In quantum systems, this landscape also allows us to define an “effective localization potential” that allows us to predict the localization region, the energies of the localized modes, the density of states, as well as the long range decay of the wave functions. I will present some experimental and numerical examples of this theory and I will show in particular how this theory has allowed to gain several orders of magnitude in computational time in semiconductor physics, in complex or disordered alloys.
