Scaling Estimates for Solutions and Dynamical Lower Bounds on Wavepacket   Spreading
  We establish quantum dynamical lower bounds for discrete one-dimensional Schr\"odinger operators in situations where, in addition to power-law upper bounds on solutions corresponding to energies in the spectrum, one also has lower bounds following a scaling law. As a consequence, we obtain improved dynamical results for the Fibonacci Hamiltonian and related models. 
David Damanik (Caltech), Serguei Tcheremchantsev (Universite   d'Orleans)