Thursday, July 4, 2013

1307.0925 (David Damanik et al.)

Almost Ballistic Transport for the Weakly Coupled Fibonacci Hamiltonian    [PDF]

David Damanik, Anton Gorodetski
We prove estimates for the transport exponents associated with the weakly coupled Fibonacci Hamiltonian. It follows in particular that the upper transport exponent $\tilde \alpha^\pm_u$ approaches the value one as the coupling goes to zero. Moreover, for sufficiently small coupling, $\tilde \alpha^\pm_u$ strictly exceeds the fractal dimension of the spectrum.
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