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An Exact Renormalization Formula for the Maryland Model

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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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Authors and Affiliations

  1. Department of Mathematical Physics, Faculty of Physics, St. Petersburg State University, Ulianovskaja, 1, St. Petersburg-Petrodvoretz, 198504, Russia

    Alexander Fedotov & Fedor Sandomirskiy

  2. Chebyshev Laboratory, St. Petersburg State University, 14th Line, 29b, Vasilyevsky Island, St. Petersburg, 199178, Russia

    Fedor Sandomirskiy

Authors
  1. Alexander Fedotov
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  2. Fedor Sandomirskiy
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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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  • DOI: https://doi.org/10.1007/s00220-014-2126-6

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