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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > The isospectral torus of quasi-periodic Schrodinger operators via periodic approximations

## The isospectral torus of quasi-periodic Schrodinger operators via periodic approximationsAdd to your list(s) Download to your calendar using vCal - Lukic, M (University of Toronto)
- Friday 10 April 2015, 15:00-15:25
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact Mustapha Amrani. Periodic and Ergodic Spectral Problems Co-authors: David Damanik (Rice University), Michael Goldstein (University of Toronto) This talk describes joint work with D. Damanik and M. Goldstein. We study quasi-periodic Schr”odinger operators $H = – rac{d The proof relies on approximation by periodic potentials $ ilde V$, which are obtained by replacing the frequency $omega$ by rational approximants $ ilde omega$. We adapt the multiscale analysis, developed by Damanik—Goldstein for $V$, so that it applies to the periodic approximants $ ilde V$. This allows us to establish estimates for gap lengths and Fourier coefficients of $ ilde V$ which are independent of period, unlike the standard estimates known in the theory of periodic Schr”odinger operators. Starting from these estimates, we obtain the main result by comparing the isospectral tori and translation flows of $ ilde V$ and $V$. 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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