---
_id: '2717'
abstract:
- lang: eng
text: 'We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions.
The matrix elements H xy, indexed by, are independent, uniformly distributed random
variables if {pipe}x-y{pipe} is less than the band width W, and zero otherwise.
We prove that the time evolution of a quantum particle subject to the Hamiltonian
H is diffusive on time scales. We also show that the localization length of the
eigenvectors of H is larger than a factor W d/6 times the band width. All results
are uniform in the size of the matrix. '
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Antti
full_name: Knowles, Antti
last_name: Knowles
citation:
ama: Erdös L, Knowles A. Quantum diffusion and eigenfunction delocalization in a
random band matrix model. Communications in Mathematical Physics. 2011;303(2):509-554.
doi:10.1007/s00220-011-1204-2
apa: Erdös, L., & Knowles, A. (2011). Quantum diffusion and eigenfunction delocalization
in a random band matrix model. Communications in Mathematical Physics.
Springer. https://doi.org/10.1007/s00220-011-1204-2
chicago: Erdös, László, and Antti Knowles. “Quantum Diffusion and Eigenfunction
Delocalization in a Random Band Matrix Model.” Communications in Mathematical
Physics. Springer, 2011. https://doi.org/10.1007/s00220-011-1204-2.
ieee: L. Erdös and A. Knowles, “Quantum diffusion and eigenfunction delocalization
in a random band matrix model,” Communications in Mathematical Physics,
vol. 303, no. 2. Springer, pp. 509–554, 2011.
ista: Erdös L, Knowles A. 2011. Quantum diffusion and eigenfunction delocalization
in a random band matrix model. Communications in Mathematical Physics. 303(2),
509–554.
mla: Erdös, László, and Antti Knowles. “Quantum Diffusion and Eigenfunction Delocalization
in a Random Band Matrix Model.” Communications in Mathematical Physics,
vol. 303, no. 2, Springer, 2011, pp. 509–54, doi:10.1007/s00220-011-1204-2.
short: L. Erdös, A. Knowles, Communications in Mathematical Physics 303 (2011) 509–554.
date_created: 2018-12-11T11:59:14Z
date_published: 2011-04-01T00:00:00Z
date_updated: 2021-01-12T06:59:15Z
day: '01'
doi: 10.1007/s00220-011-1204-2
extern: 1
intvolume: ' 303'
issue: '2'
month: '04'
page: 509 - 554
publication: Communications in Mathematical Physics
publication_status: published
publisher: Springer
publist_id: '4175'
quality_controlled: 0
status: public
title: Quantum diffusion and eigenfunction delocalization in a random band matrix
model
type: journal_article
volume: 303
year: '2011'
...