COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

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
- Featured lists
- INI info aggregator
- Isaac Newton Institute Seminar Series
- School of Physical Sciences
- Seminar Room 1, Newton Institute
- bld31
Note that ex-directory lists are not shown. |
## Other listsdh539 The Cambridge Globalist Gates Distinguished Lecture Series Greece and its History AI+Pizza## Other talksCANCELLED - Mathematical methods in reacting flows: From spectral to Lyapunov analysis Making a Crowdsourced Task Attractive: Measuring Workers Pre-task Interactions Interconversion of Light and Electricity in Molecular Semiconductors The persistence and transience of memory Polynomial approximation of high-dimensional functions on irregular domains The importance of seed testing |