An Exact Renormalization Formula for the Maryland Model

Abstract

We discuss the difference Schrödinger equation \({\psi_{k+1}+\psi_{k-1}+\lambda \cot(\pi(\omega k+\theta))\psi_k=E\psi_k}\), \({k \in \mathbb{Z}}\), where \({\lambda}\), \({\omega}\), \({\theta}\) and E are parameters. We obtain explicit renormalization formulas relating its solutions for large \({|k|}\) to solutions of the equation with new parameters \({\lambda}\), \({\omega}\), \({\theta}\) and E for bounded \({|k|}\). These formulas are similar to the renormalization formulas from the theory of Gaussian exponential sums.

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Correspondence to Fedor Sandomirskiy.

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Communicated by B. Simon

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Fedotov, A., Sandomirskiy, F. An Exact Renormalization Formula for the Maryland Model. Commun. Math. Phys. 334, 1083–1099 (2015). https://doi.org/10.1007/s00220-014-2126-6

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Keywords

  • Difference Equation
  • Meromorphic Function
  • Trigonometric Polynomial
  • Integration Contour
  • Minimal Solution