The Fibonacci Hamiltonian
نویسندگان
چکیده
منابع مشابه
Uniform Dynamical Bounds for the Fibonacci Hamiltonian
We prove quantum dynamical upper bounds for operators from the Fibonacci hull. These bounds hold for sufficiently large coupling and they are uniform in the phase. This extends recent work by Killip, Kiselev and Last who obtained these bounds for one particular phase. The main ingredient in our proof is a detailed combinatorial analysis of the sequences in the Fibonacci hull.
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متن کاملThe Spectrum of the Weakly Coupled Fibonacci Hamiltonian
We consider the spectrum of the Fibonacci Hamiltonian for small values of the coupling constant. It is known that this set is a Cantor set of zero Lebesgue measure. Here we study the limit, as the value of the coupling constant approaches zero, of its thickness and its Hausdorff dimension. We announce the following results and explain some key ideas that go into their proofs. The thickness tend...
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We consider the trace map associated with the Fibonacci Hamiltonian as a diffeomorphism on the invariant surface associated with a given coupling constant and prove that the non-wandering set of this map is hyperbolic if the coupling is sufficiently small. As a consequence, for these values of the coupling constant, the local and global Hausdorff dimension and the local and global box counting ...
متن کاملThe Density of States Measure of the Weakly Coupled Fibonacci Hamiltonian
We consider the density of states measure of the Fibonacci Hamiltonian and show that, for small values of the coupling constant V , this measure is exact-dimensional and the almost everywhere value dV of the local scaling exponent is a smooth function of V , is strictly smaller than the Hausdorff dimension of the spectrum, and converges to one as V tends to zero. The proof relies on a new conne...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2016
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-016-0660-x