Cesar R. de Oliveira, Roberto A. Prado 
Quantum Hamiltonians with Quasi-Ballistic Dynamics and Point Spectrum
(348K, pdf)

ABSTRACT.  Consider the family of Schr\"o\-dinger operators (and 
also its Dirac version) on 
$\ell^2(\mathbb{Z})$ or $\ell^2(\mathbb{N})$ 
\[ H^W_{\omega,S}=\Delta + \lambda F(S^n\omega) + W , \quad 
\omega\in\Omega , 
\] 
 where $S$ is a transformation on (compact metric) 
$\Omega$, $F$ a real Lipschitz function and $W$ a (sufficiently fast) 
power-decaying perturbation. Under 
certain conditions it is shown that $H^W_{\omega,S}$ presents 
quasi-ballistic dynamics for 
$\omega$ in a dense $G_{\delta}$ set. Applications include potentials 
generated by rotations of the torus 
with analytic condition on $F$, doubling map, Axiom~A dynamical systems 
and the Anderson model. If $W$ 
is a rank one perturbation, examples of $H^W_{\omega,S}$ with 
quasi-ballistic dynamics and 
 point spectrum are also presented.