# Anderson localization - in depth



## [50 years of Anderson Localization](https://repository.library.northeastern.edu/files/neu:f1881w02j/fulltext.pdf)


## 1971 Ambegaokar-Halperin-Langer [Hopping Conductivity in Disordered Systems](https://moodle.technion.ac.il/pluginfile.php/1106168/mod_resource/content/1/Ambegaokar_Halperin_Langer_PhysRevB.4.2612.pdf)


## Economou 1971 [localized phonons](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5452/economou.pdf)

- [Anderson localization of ultrasound in three dimensions](http://www2.physics.umanitoba.ca/u/jhpage/PDF_Files/Page_UltrasoundLocalization_Varenna.pdf) J. H. Page

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](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5453/mott%2Bmobility%2Bedge.pdf)

> [There is a simple argument due to Mott that shows that extended and localized states should not both exist at the same energy](https://knowen.org/nodes/999) 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](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5472/extended%2Band%2Blocalized.pdf)
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](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.6.3598)



## 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://knowen-production.s3.amazonaws.com/uploads/attachment/file/5451/levitov.pdf)

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

- Oleg Utesov https://arxiv.org/pdf/2203.12305.pdf

# Parents

* Anderson Localization

# Attachments

* [](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5451/levitov.pdf)
* [](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5452/economou.pdf)
* [](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5453/mott%2Bmobility%2Bedge.pdf)
* [](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5472/extended%2Band%2Blocalized.pdf)