Dynamical Upper Bounds for the Fibonacci Hamiltonian
Disordered Systems and Neural Networks
2007-05-23 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
We consider transport exponents associated with the dynamics of a wavepacket in a discrete one-dimensional quantum system and develop a general method for proving upper bounds for these exponents in terms of the norms of transfer matrices at complex energies. Using this method, we prove such upper bounds for the Fibonacci Hamiltonian. Together with the known lower bounds, this shows that these exponents are strictly between zero and one for sufficiently large coupling and the large coupling behavior follows a law predicted by Abe and Hiramoto.
Cite
@article{arxiv.cond-mat/0502004,
title = {Dynamical Upper Bounds for the Fibonacci Hamiltonian},
author = {David Damanik and Serguei Tcheremchantsev},
journal= {arXiv preprint arXiv:cond-mat/0502004},
year = {2007}
}
Comments
4 pages