|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Statistics of anomalously localized states at the center of band E=0 in the one-dimensional Anderson localization model | | V.E.Kravtsov
; V.I.Yudson
; | | Date: |
23 Aug 2012 | | Abstract: | We consider the distribution function $P(|psi|^{2})$ of the eigenfunction
amplitude at the center-of-band (E=0) anomaly in the one-dimensional
tight-binding chain with weak uncorrelated on-site disorder (the
one-dimensional Anderson model). The special emphasis is on the probability of
the anomalously localized states (ALS) with $|psi|^{2}$ much larger than the
inverse typical localization length $ell_{0}$. Using the solution to the
generating function $Phi_{an}(u,phi)$ found recently in our works we find the
ALS probability distribution $P(|psi|^{2})$ at $|psi|^{2}ell_{0} >> 1$. As
an auxiliary preliminary step we found the asymptotic form of the generating
function $Phi_{an}(u,phi)$ at $u >> 1$ which can be used to compute other
statistical properties at the center-of-band anomaly. We show that at
moderately large values of $|psi|^{2}ell_{0}$, the probability of ALS at E=0
is smaller than at energies away from the anomaly. However, at very large
values of $|psi|^{2}ell_{0}$, the tendency is inverted: it is exponentially
easier to create a very strongly localized state at E=0 than at energies away
from the anomaly. We also found the leading term in the behavior of
$P(|psi|^{2})$ at small $|psi|^{2}<< ell_{0}^{-1}$ and show that it is
consistent with the exponential localization corresponding to the Lyapunov
exponent found earlier by Kappus and Wegner and Derrida and Gardner. | | Source: | arXiv, 1208.4789 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER