Dynamical Upper Bounds for the Fibonacci Hamiltonian

Details Dynamical Upper Bounds for the Fibonacci Hamiltonian Dynamical Upper Bounds for the Fibonacci Hamiltonian

2005-01-31

arxiv.org/abs/cond-mat/0502004v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages

Scientific paper

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.

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