Talk:Anderson localization

message: I've created a new section to separate the edit of 75.85.165.206.  Anderson localization may have been studied by mathematicians before physicists (you could say that about much of physics), but this particular description appears to be original research.  In any case, a good clean-up is necessary.
Cdion 10:08, 17 September 2007 (UTC)
replies: text: I've seen it in both contexts. Physicists tend to talk about semiconductors and physical models. Mathematicians try to find exact solutions to the discrete Laplace operator or rather the discrete Schrodinger operator.  Even the one-dimensional case appears to be a challenge: They have managed to find solutions for two cases: periodic potentials which have travelling waves; also bandgaps, and the localized case (which was explicitly called 'Anderson localization' in the colloqium I went to), but they are still struggling with certain cases in between (where the potential is pseudo-periodic). Short of a full solution, the goal is to characterize the spectral gap. linas (talk) 06:03, 8 September 2008 (UTC)

text: Below follows the long rant that was added by User:75.85.165.206 In Sept. 2007. I copied it here because its an interesting rant.  linas (talk) 06:15, 8 September 2008 (UTC)
thread_title:  Mathematics 

message: I think several important parts are missing:
* definition of Anderson Hamiltonian (note that the article "Anderson model" is about something different)
* some explanation (or ref.) to what are localised and extended states
* summary of mathematically rigorous results: localisation in 1D (Goldsheid-Molchanov-Pastur ...), and in arbitrary dimension for high energy/high disorder (Frohlich-Spencer ...)
This looks like a major revision, so it would be nice to have some discussion here before starting it.
Sasha (talk) 00:27, 16 June 2011 (UTC)
thread_title:  Revision? 

message: The page should updated to include the result described in http://news.illinois.edu/news/11/1007waves_BrianDeMarco.html
I am not qualified to make this update.  — Preceding unsigned comment added by 76.115.88.202 (talk) 02:35, 10 December 2012 (UTC)
thread_title:  New Result 

message: This article says V must drop off as 1/r^2 for localisation to occur, but the original article by Anderson has V dropping off faster than 1/r^3 with special behaviour in the exact 1/r^3 case. Which is correct? There's not citation for the claim here. Jaredjeya (talk) 21:19, 27 April 2018 (UTC)
thread_title:  Dropoff of V(r) 

message: Apparently (defect-free) quasicrystals can localize light as well, as has just been shown experimentally by Sinelnik et al.. This is especially interesting, as we do not have randomness here, but rather aperiodic "pseudo-randomness". I feel just as unqualified to update the article as the IP from 2012 in the talk section above sadly. --2003:CC:370B:9636:D58A:F5E5:6F35:74C2 (talk) 09:03, 11 November 2020 (UTC)
thread_title:  Newer Result 

message: It would be good to have formal definitions of all the variables, like W, and D etc  — Preceding unsigned comment added by 89.114.64.121 (talk) 21:10, 5 February 2023 (UTC)
replies: text: and Ψ_i in the Introduction (localized wave function ? it is not said that i, j, k are sites of a lattice) Lau 00 (talk) 11:09, 22 June 2023 (UTC)
replies: text: Solutions to the Schrodinger eqn are called wave functions. The j,k are lattice locations. I updated the article to state this. 67.198.37.16 (talk) 23:26, 16 May 2024 (UTC)
thread_title:  Definitions of variables 

message: One section states:
:Direct numerical solution of Maxwell equations to demonstrate Anderson localization of light has been implemented (Conti and Fratalocchi, 2008).
but a later section states:
:The existence of Anderson localization for light in 3D was debated for years (Skipetrov et al., 2016) and remains unresolved today.
Perhaps the earlier result is not for 3D? The critical dimension is 2, so ??? I guess the point here is that light is a vector, not a scalar? Why would vector vs. scalar make a difference? ??? 67.198.37.16 (talk) 23:56, 16 May 2024 (UTC)
thread_title:  Is light localized or not?