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arXiv · 0906.1932

Dynamical Bounds for Sturmian Schr\"{o}dinger Operators

L. Marin
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Abstract

The Fibonacci Hamiltonian, that is a Schr\"{o}dinger operator associated to a quasiperiodical sturmian potential with respect to the golden mean has been investigated intensively in recent years. Damanik and Tcheremchantsev developed a method and find a non trivial dynamical upper bound for this model. In this paper, we use this method to generalize to a large family of Sturmian operators dynamical upper bounds and show at sufficently large coupling anomalous transport for operators associated to irrational number with a generic diophantine condition. As a counter example, we exhibit a pathological irrational number which do not verify this condition and show its associated dynamic exponent only has ballistic bound. Moreover, we establish a global lower bound for the lower box counting dimension of the spectrum that is used to obtain a dynamical lower bound for bounded density irrational numbers.

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L. Marin. 2009-06-10. Dynamical Bounds for Sturmian Schr\"{o}dinger Operators. https://doi.org/10.1142/s0129055x10004090

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