Sommaire:

In complex or disordered media, standing waves can undergo a strange phenomenon that has intrigued physicists and mathematicians for over 60 years, known as “wave localization.” It consists in a concentration of the wave energy in a very restricted sub-region of the complete domain. This localization has major consequences not only on the vibration but also the propagation properties of the system, in particular electronic transport in disordered alloys. It has been demonstrated experimentally in mechanics, acoustics, electromagnetics and quantum physics. In this talk, we will present a theory that highlights the existence of an underlying and universal structure, the localization landscape, obtained by solving a problem associated with the wave equation [1]. In quantum systems, this landscape makes it possible to define an “effective potential” that predicts the localization subregions, the energies of localized modes, the density of states and the long-range decay of wave functions, regardless of the dimension, both in continuous and discrete settings. Finally, we will provide an overview of the applications of this theory to mechanics, semiconductor physics, as well as for molecular and cold atom systems. [1] M. Filoche & S. Mayboroda, PNAS (2012) LF9:14761-14766.

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