Phase transitions Anderson localization

It is not clear, whether the experimentally observed random local freezing of the deuterons in the O-D—O bonds in deuteron glasses corresponds to a true thermodynamic phase transition or whether one deals with a dynamic phenomenon which only seems static because of the finite observation time of the experimental techniques. The recently observed42 splitting between the field-cooled and zero-field dielectric susceptibilities below an instability temperature Tf seems to speak for the occurrence of an Almeida-Thouless-like thermodynamic phase transition in deuteron glasses. It is well known that ID NMR and EPR allow a direct measurement of the Edwards-Anderson order parameter qEA only on time scales of 10 3-10 8 s and 2D exchange NMR possibly seems to be a better technique for such slow motions. 

Apparently, in the near future there will be developed (a) a detailed theory of surface excitons not only at the crystal boundary with vacuum but also at the interfaces of various condensed media, particularly of different symmetry (b) a theory of surface excitons including the exciton-phonon interaction and, in particular, the theory of self-trapping of surface excitons (c) the features of surface excitons for quasi-one-dimensional and quasi-two-dimensional crystals (d) the theory of kinetic parameters and, particularly, the theory of diffusion of surface excitons (e) the theory of surface excitons in disordered media (f) the features of Anderson localization on a surface (g) the theory of the interaction of surface excitons of various types with charged and neutral particles (h) the evaluation of the role of surface excitons in the process of photoelectron emission (i) the electronic and structural phase transitions on the surface with participation of surface excitons. We mention here also the theory of exciton-exciton interactions at the surface, the surface biexcitons, and the role of defects (see, as example, (53)). The above list of problems reflects mainly the interests of the author and thus is far from complete. Referring in one or another way to surface excitons we enter into a large, interesting, and yet insufficiently studied field of solid-state physics. 

These experimental findings for low-frequency electromagnetic response are in contrast with the expectations for the Anderson IMT [99] in which electronic behavior is controlled by disorder. In the dielectric phase, electrons are bound by fluctuations of the random potential. On the metallic side of the transition, free carriers have short scattering times. In the metallic phase near the transition s is positive because the disorder causes dynamic polarization due to slowing diffusion due to localization effects. When approaching the IMT transition the localization effects increase and s diverges (dielectric catastrophe [120]). 

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