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Weak Localization, Anderson Localization and disorder

by jbar18
Tags: anderson, disorder, localization, weak
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jbar18
#1
Jan3-14, 04:04 AM
P: 53
Hey,

I was wondering if anybody could give me a brief overview (if possible) of how weak localization differs from strong localization, and any rigorous definitions of "disorder" and "localization" (if they exist) and perhaps recommend some good papers to read on the subject.

Thanks
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jbar18
#2
Jan3-14, 06:09 AM
P: 53
Having looked back at my question, I feel that the first part was poorly asked. I will try to be more specific.

As I understand, Anderson localization is the absence of diffusion of waves caused by disordered boundary conditions. This translates to waves exponentially decaying away from points where they are localized (right so far?). So now where does weak localization fit in? I would naively presume that it sits somewhere between unhindered propagation and being strongly localized, but what does that mean? A linear decay rather than exponential?

To me, Anderson localization is reasonably accessible because it is general to all waves, however I have only seen weak localization talked about in the context of electrons. For example, I found a beautiful picture showing Anderson localization in water waves. Metal nuts were placed in a shallow pool and waves were excited, and when the nuts were arranged like a lattice the waves propagated across all of the water, whereas when they were arranged more randomly, the waves were localized around the nuts. Can weak localization be visualised in a similar way?

Again, if somebody could point me to any papers they think are very good I would be grateful. Obviously there's plenty out there, but if anybody knows of any really good introductory ones off the top of their head that would be great.

Thanks again.
ZapperZ
#3
Jan3-14, 07:58 AM
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I can give you, in case you haven't come across it yet, the Physics Today elementary-level overview of Anderson localization. It should have the relevant references that you might want to check out if you need more in-detail information.

http://ps.nano-cops.com/sites/defaul...calization.pdf

Zz.

jbar18
#4
Jan4-14, 05:53 AM
P: 53
Weak Localization, Anderson Localization and disorder

Can anyone tell me if there is a rigorous definition of disorder or not (or localization, for that matter)? At the moment I am working on the assumption that they are kind of hand wavy concepts.


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