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res:
bibo_abstract:
- We consider Hermitian and symmetric random band matrices H in d ≥ dimensions.
The matrix elements Hxy, indexed by x,y ∈ Λ ⊂ ℤd are independent and their variances
satisfy σ2xy:= E{pipe}Hxy{pipe}2 = W-d f((x-y)/W for some probability density
f. We assume that the law of each matrix element Hxy is symmetric and exhibits
subexponential decay. We prove that the time evolution of a quantum particle subject
to the Hamiltonian H is diffusive on time scales ≪ Wd/3. We also show that the
localization length of the eigenvectors of H is larger than a factor Wd/6 times
the band width W. All results are uniform in the size {pipe}Λ{pipe} of the matrix.
This extends our recent result (Erdo{double acute}s and Knowles in Commun. Math.
Phys., 2011) to general band matrices. As another consequence of our proof we
show that, for a larger class of random matrices satisfying Σx σ2xy for all y,
the largest eigenvalue of H is bounded with high probability by 2+M-2/3+e{open}
for any e{open} > 0, where M:= 1/(maxx,y σ2xy).@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
bibo_doi: 10.1007/s00023-011-0104-5
bibo_issue: '7'
bibo_volume: 12
dct_date: 2011^xs_gYear
dct_publisher: Birkhäuser@
dct_title: Quantum diffusion and delocalization for band matrices with general distribution@
...