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What is the exact point of Anderson's localization paper?

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Today, the idea of Anderson localization (as far as i understand) is that, in a disordered system, there are some localized single-particle eigenstates. Especially, in 1d and 2d, there are exclusively only such states.

But, isn't it obvious that a defect potential in some periodic potential can induce defect modes? Actually, if you lower the potential of some site in a periodic tight-binding model, you create a defect mode, which can be solved analytically easily.

So, what was the exact idea of Anderson?

This post imported from StackExchange Physics at 2015-12-27 11:23 (UTC), posted by SE-user John
asked Dec 26, 2015 in Theoretical Physics by John (25 points) [ no revision ]
Sure, if there is only one single deep potential well, classically electrons can be localized. But what Anderson dealt with is a disordered potential, meaning that one has to average over all disorder configurations, taking into account the competing kinetic energy of electrons. The fact that in 3D, a critical strength of disorder is needed for localization to happen shows that localization is really a nontrivial effect.

This post imported from StackExchange Physics at 2015-12-27 11:23 (UTC), posted by SE-user Meng Cheng
Can you try to ask a more well-defined question? I'm not sure what you're looking for - an explanation of Anderson localization, an explanation why it is physically interesting, or something else?

This post imported from StackExchange Physics at 2015-12-27 11:23 (UTC), posted by SE-user ACuriousMind
@ACuriousMind My point is, what is the non-trivial point of Anderson in his original paper? Localization by defect is trivial.

This post imported from StackExchange Physics at 2015-12-27 11:23 (UTC), posted by SE-user John

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