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Title: Renormalization of wave function fluctuations for a generalized Harper equation
Author(s): Hulton, Sarah
Supervisor(s): Mestel, Ben
Keywords: renormalization
Issue Date: Nov-2006
Publisher: University of Stirling
Abstract: A renormalization analysis is presented for a generalized Harper equation (1 + α cos(2π(ω(i + 1/2) + φ)))ψi+1 + (1 + α cos(2π(ω(i − 1/2) + φ)))ψi−1 +2λ cos(2π(iω + φ))ψi = Eψi. (0.1) For values of the parameter ω having periodic continued-fraction expansion, we construct the periodic orbits of the renormalization strange sets in function space that govern the wave function fluctuations of the solutions of the generalized Harper equation in the strong-coupling limit λ→∞. For values of ω with non-periodic continued fraction expansions, we make some conjectures based on work of Mestel and Osbaldestin on the likely structure of the renormalization strange set.
Type: Thesis or Dissertation
Affiliation: School of Natural Sciences
Computing Science and Mathematics

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