2005/01/31 by David Damanik, Damanik, David, Serguei Tcheremchantsev +1
Mathematics · Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #cond-mat.dis-nn #math-ph #math.DS #math.MP
paper · pdf · doi:10.48550/arxiv.cond-mat/0502004
4 pages
arxiv created 2005/01/31 · openalex publication_date 2005/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.