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Dynamical self-averaging for a lattice Schr\"odinger equation with weak random potential by Butz, Maximilian is a scholarly article available to read on EtoBox.

What is Dynamical self-averaging for a lattice Schr\"odinger equation with weak random potential about?

We study the kinetic, weak coupling limit of the dynamics governed by a discrete random Schr\"odinger operator on $\mathbb{Z}^3$. For sequences of $\ell^2\left(\mathbb{Z}^3\right)$-bounded initial states and convergent initial Wigner transform, we prove that the scaled Wigner transform converges to the solution of a linear Boltzmann equation in $L^r\left(\mathbb{P}\right)$for all $r>0$, thus considerably strengthening a previous result by Chen. The key ingredients for the proof are a finer classification of graphs in the expansion of the perturbed dynamics as well as a novel resolvent estimate for the unperturbed Schr\"odinger operator. Under some additional assumption on the sequence of initial states we even prove almost sure convergence.

Author

Butz, Maximilian

Published

2013

Language

EN