Power law growth for the resistance in the Fibonacci model |
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Authors: | B Iochum D Testard |
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Institution: | (1) Centre de Physique Théorique (Unité Propre de Recherche 7061), CNRS Luminy, Case 907, F 13288 Marseille Cedex 9, France;(2) Université de Provence, Marseille, France;(3) Université d'Aix-Marseille II, Luminy, France |
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Abstract: | Many one-dimensional quasiperiodic systems based on the Fibonacci rule, such as the tight-binding HamiltonianH(n)=(n+1)+(n–1)+v(n)
(n),n,l
2(),, wherev(n)=(n+1)]–n],x] denoting the integer part ofx and the golden mean
, give rise to the same recursion relation for the transfer matrices. It is proved that the wave functions and the norm of transfer matrices are polynomially bounded (critical regime) if and only if the energy is in the spectrum of the Hamiltonian. This solves a conjecture of Kohmoto and Sutherland on the power-law growth of the resistance in a one-dimensional quasicrystal. |
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Keywords: | Periodic Hamiltonian Fibonacci chain transfer matrix |
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