Speaker: 

Professor Lazlo Erdoes

Institution: 

University Munich, visiting Harvard

Time: 

Thursday, January 26, 2006 - 2:00pm

Location: 

MSTB 254

We study the extended states regime of the discrete Anderson model. The perturbative approach requires precise estimates on the free propagator,
$(a- e(p)+i\eta)^{-1}$,$\eta>0$, $\alpha\in \bR$,
where $e(p)= \sum_{i=1}^3 [1- \cos (p_i)]$, $p=(p_1, p_2, p_3)$,
is the dispersion relation of the three dimensional cubic lattice. The level surfaces of the function $e(p)$ have vanishing curvature. We will present new bounds on the Fourier transform of such surfaces. This will yield estimates on the probability that
a quantum particle travelling in a weak random environment
recollides with obstacles visited earlier.