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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Maryland equation, renormalization formulas and mimimal meromorphic solutions to difference equations

## Maryland equation, renormalization formulas and mimimal meromorphic solutions to difference equationsAdd to your list(s) Download to your calendar using vCal - Fedotov, A (Saint Petersburg State University)
- Friday 27 March 2015, 15:00-16:00
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Periodic and Ergodic Spectral Problems Co-author: Fedor Sandomirskyi (Saint Petersburg State University) Consider the difference Schrödinger equation $psi_{k+1}psi_{k-1}+lambda {cotan} (piomega k heta)psi_k=Epsi_k,quad kin{mathbb Z}$,where $lambda$, $omega$, $ heta$ and $E$ are parameters. If $omega$ is irrational, this equation is quasi-periodic. It was introduced by specialists in solid state physics from Maryland and is now called the Maryland equation. Computer calculations show that, for large $k$, its eigenfunctions have a multiscale, “mutltifractal” structure. We obtained renormalization formulas that express the solutions to the input Marryland equation for large $k$ in terms of solutions to the Marryland equation with new parameters for bounded $k$. The proof is based on the theory of meromorphic solutions of difference equations on the complex plane, and on ideas of the monodromization met hod—the renormalization approach first suggested by V.S.Buslaev and A.A. Fedotov. Our formulas are close to the renormalization formulas from the theory
of the Gaussian exponential sums $S(N)= um_{n=0} This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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