Power-Law Bounds on Transfer Matrices and Quantum Dynamics in One   Dimension
  We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schr\"odinger operators which is based on power-law bounds on transfer matrices. It suffices to have such bounds for a nonempty set of energies. We apply this result to various models, including the Fibonacci Hamiltonian. 
David Damanik (Caltech), Serguei Tcheremchantsev (Universite   d'Orleans)