Dynamical bounds for Sturmian Schrödinger operators |
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Institution: | UMR 6628-MAPMO, Université d''Orléans, B.P. 6759, 45067 Orléans cedex, France |
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Abstract: | The Fibonacci Hamiltonian, that is a Schrödinger operator associated to a Sturmian potential with respect to the golden number has been investigated intensively in recent years. Damanik and Tcheremchantsev developed a method and found a non-trivial dynamical upper bound for transport exponents for this model. This method can be generalized to obtain results for almost all irrational numbers. As a counter example, we exhibit a pathological irrational number with no possible better bound. Moreover, we establish a global lower bound for the lower box dimension of the spectrum that could be used to obtain a dynamical lower bound for irrational numbers with bounded density. To cite this article: L. Marin, C. R. Acad. Sci. Paris, Ser. I 346 (2008). |
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