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res:
bibo_abstract:
- We consider Hermitian and symmetric random band matrices H = (h xy ) in d⩾1 d
⩾ 1 dimensions. The matrix entries h xy , indexed by x,y∈(Z/LZ)d x , y ∈ ( Z /
L Z ) d , are independent, centred random variables with variances sxy=E|hxy|2
s x y = E | h x y | 2 . We assume that s xy is negligible if |x − y| exceeds the
band width W. In one dimension we prove that the eigenvectors of H are delocalized
if W≫L4/5 W ≫ L 4 / 5 . We also show that the magnitude of the matrix entries
|Gxy|2 | G x y | 2 of the resolvent G=G(z)=(H−z)−1 G = G ( z ) = ( H - z ) - 1
is self-averaging and we compute E|Gxy|2 E | G x y | 2 . We show that, as L→∞
L → ∞ and W≫L4/5 W ≫ L 4 / 5 , the behaviour of E|Gxy|2 E | G x y | 2 is governed
by a diffusion operator whose diffusion constant we compute. Similar results are
obtained in higher dimensions.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: László
foaf_name: László Erdös
foaf_surname: Erdös
foaf_workInfoHomepage: http://www.librecat.org/personId=4DBD5372-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0001-5366-9603
- foaf_Person:
foaf_givenName: Antti
foaf_name: Knowles, Antti
foaf_surname: Knowles
- foaf_Person:
foaf_givenName: Horng
foaf_name: Yau, Horng-Tzer
foaf_surname: Yau
- foaf_Person:
foaf_givenName: Jun
foaf_name: Yin, Jun
foaf_surname: Yin
bibo_doi: 10.1007/s00220-013-1773-3
bibo_issue: '1'
bibo_volume: 323
dct_date: 2013^xs_gYear
dct_publisher: Springer@
dct_title: Delocalization and diffusion profile for random band matrices@
...