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

+ 1 like - 0 dislike
487 views

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
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

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysic$\varnothing$OverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.