# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.331994

Acta Mathematica, 200, (2), 211-277, 2006.4
We consider random Schrödinger equations on$R$^{$d$}for$d$≽ 3 with a homogeneous Anderson–Poisson type random potential. Denote by λ the coupling constant and $\psi_t$ the solution with initial data $\psi_0$ . The space and time variables scale as $x\sim\lambda ^{{ - 2 - \varkappa/2}} {\text{ and }}t\sim\lambda ^{{ - 2 - \varkappa}} {\text{ with }}0 < \varkappa < \varkappa_{0} {\left( d \right)}$ . We prove that, in the limit λ → 0, the expectation of the Wigner distribution of $\psi_t$ converges weakly to the solution of a heat equation in the space variable$x$for arbitrary$L$^{2}initial data.
@inproceedings{lászló2006quantum,
title={Quantum diffusion of the random Schrödinger evolution in the scaling limit},
author={László Erdős, Manfred Salmhofer, and Horng-Tzer Yau},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203351955696703},
booktitle={Acta Mathematica},
volume={200},
number={2},
pages={211-277},
year={2006},
}

László Erdős, Manfred Salmhofer, and Horng-Tzer Yau. Quantum diffusion of the random Schrödinger evolution in the scaling limit. 2006. Vol. 200. In Acta Mathematica. pp.211-277. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203351955696703.