Communications in Mathematical Physics

, Volume 334, Issue 2, pp 1083–1099 | Cite as

An Exact Renormalization Formula for the Maryland Model



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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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Mathematical Physics, Faculty of PhysicsSt. Petersburg State UniversitySt. Petersburg-PetrodvoretzRussia
  2. 2.Chebyshev LaboratorySt. Petersburg State UniversitySt. PetersburgRussia

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