Anderson Localization: Decoherence Explanation?

[Descartz2000]

Is decoherence the best way to explain the phenomenon of Anderson Localization?

 

[MGH]

I don't think so. Anderson localization is a coherent interference effect.
one way to explain it is as follows - think of a quantum particle released inside a disordered medium at point A. The amplitude for that particle to reach to a distant point B in the medium is a sum of all possible paths from A to B. in a disordered medium each path is accompanied with a different (random) phase and therefore you get random interference, and the particle shows diffusion. but this is not Anderson Localization.

Localization kicks in when you take into account the paths that lead from A back to A. there are many such paths of course, but they come in pairs: from A to A in a loop, and from A to A in the same loop but in the opposite direction. Note that such pairs do not exist for paths from A to a different point B. The point is that the two reversed loops from A to A are accompanied with exactly the same phase! - it is the same path, only reversed. as a result, the particle has a constructive interference to remain in point A - the origin. You can show, that as disorder is increased, the number of such loops increases very sharply. this is the correction to diffusion that leads to Anderson localization.

 

[xepma]

That's a nice explanation MGH. Do you happen to know some introductory material into the subject? (graduate level)

 

[sokrates]

Anderson Localization and Its Ramifications: Disorder, Phase Coherence and Electron Correlation

Springer 2003

If you are familiar with the second quantization treatment, maybe not quite an intro. book - but solid.