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Anderson localization - in depth

50 years of Anderson Localization

1971 Ambegaokar-Halperin-Langer Hopping Conductivity in Disordered Systems

Economou 1971 localized phonons

This paper summarizes recent progress in demonstrating the localization of ultrasound in a “mesoglass” made by assembling aluminum beads into a disordered three-dimensional elastic network

During the 1980s, it was realized that Anderson localization [1, 2] - the spatial trapping of waves due to disorder - is not only a quantum effect, but is, more generally, a phenomenon that may occur for any type of wave: quantum or classical

Mott - mobility edge - 1967-1987

There is a simple argument due to Mott that shows that extended and localized states should not both exist at the same energy in a generic random potential. Therefore there is a "mobility edge": there is a particular energy Ec above which eigenstates are extended, and below which eigenstates are localized. The argument is that if both extended and localized states were present at the same energy, then because the energy denominator is zero, even a small perturbation would strongly mix the extended and localized states, giving two extended states.

Overview on Some Aspects of the Theory of Localization
BY A. BREZINI and N. ZEKRI

It is generally believed that localized and extended states with the same energy do not exist: the main argument is that
admixture would delocalize the former but without any rigorous proof [32]. Recently,
Srivastava [33] has cast doubt on this point by examining the possibility

confluence states ...where the random potential can become infinite at some sites with a given probability. In such models, a special class of localized states has been reported: “the molecular states” which are not only localized but appear at energies which are dense in the spectrum 35

Delocalization due to interactions

  • levitov

physical implication for Q-SNS is not useful (unclear) because delocalization is predicted.
LEEs are localized because LEEs do not contribute to the thermal conductivity.

Delocalization of Vibrational Modes Caused by Electric Dipole Interaction

https://arxiv.org/pdf/cond-mat/9609132.pdf