, Volume 236, Issue 3, pp 513-534

Power-Law Bounds on Transfer Matrices and Quantum Dynamics in One Dimension

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Abstract:

 We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schrödinger 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.

Received: 5 June 2002 / Accepted: 20 January 2003 Published online: 28 March 2003
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ID="⋆" D.D. was supported in part by NSF Grant No. DMS–0227289
Communicated by M. Aizenman