---
_id: '2751'
abstract:
- lang: eng
text: We consider random Schrödinger equations on ℤd for d ≥ 3 with identically
distributed random potential. Denote by λ the coupling constant and ψ t the solution
with initial data ψ 0. The space and time variables scale as x ∼ λ -2-κ/2,t ∼
λ-2-κ with 0 < κ < κ0(d). We prove that, in the limit λ → 0, the expectation
of the Wigner distribution of ψ t converges weakly to a solution of a heat equation
in the space variable x for arbitrary L 2 initial data. The diffusion coefficient
is uniquely determined by the kinetic energy associated to the momentum υ. This
work is an extension to the lattice case of our previous result in the continuum
[8,9]. Due to the non-convexity of the level surfaces of the dispersion relation,
the estimates of several Feynman graphs are more involved.
author:
- first_name: László
full_name: László Erdös
id: 4DBD5372-F248-11E8-B48F-1D18A9856A87
last_name: Erdös
orcid: 0000-0001-5366-9603
- first_name: Manfred
full_name: Salmhofer, Manfred
last_name: Salmhofer
- first_name: Horng
full_name: Yau, Horng-Tzer
last_name: Yau
citation:
ama: Erdös L, Salmhofer M, Yau H. Quantum diffusion for the Anderson model in the
scaling limit. Annales Henri Poincare. 2007;8(4):621-685. doi:10.1007/s00023-006-0318-0
apa: Erdös, L., Salmhofer, M., & Yau, H. (2007). Quantum diffusion for the Anderson
model in the scaling limit. Annales Henri Poincare. Birkhäuser. https://doi.org/10.1007/s00023-006-0318-0
chicago: Erdös, László, Manfred Salmhofer, and Horng Yau. “Quantum Diffusion for
the Anderson Model in the Scaling Limit.” Annales Henri Poincare. Birkhäuser,
2007. https://doi.org/10.1007/s00023-006-0318-0.
ieee: L. Erdös, M. Salmhofer, and H. Yau, “Quantum diffusion for the Anderson model
in the scaling limit,” Annales Henri Poincare, vol. 8, no. 4. Birkhäuser,
pp. 621–685, 2007.
ista: Erdös L, Salmhofer M, Yau H. 2007. Quantum diffusion for the Anderson model
in the scaling limit. Annales Henri Poincare. 8(4), 621–685.
mla: Erdös, László, et al. “Quantum Diffusion for the Anderson Model in the Scaling
Limit.” Annales Henri Poincare, vol. 8, no. 4, Birkhäuser, 2007, pp. 621–85,
doi:10.1007/s00023-006-0318-0.
short: L. Erdös, M. Salmhofer, H. Yau, Annales Henri Poincare 8 (2007) 621–685.
date_created: 2018-12-11T11:59:24Z
date_published: 2007-07-01T00:00:00Z
date_updated: 2021-01-12T06:59:27Z
day: '01'
doi: 10.1007/s00023-006-0318-0
extern: 1
intvolume: ' 8'
issue: '4'
month: '07'
page: 621 - 685
publication: Annales Henri Poincare
publication_status: published
publisher: Birkhäuser
publist_id: '4141'
quality_controlled: 0
status: public
title: Quantum diffusion for the Anderson model in the scaling limit
type: journal_article
volume: 8
year: '2007'
...