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 > One-dimensional quasi-periodic Schrdinger operators V

## One-dimensional quasi-periodic Schrdinger operators VAdd to your list(s) Download to your calendar using vCal - Marx, C (Oberlin College)
- Friday 16 January 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 Quasi-periodic Schrdinger operators arise in solid state physics, describing the influence of an external magnetic field on the electrons of a crystal. In the late 1970s, numerical studies for the most prominent model, the almost Mathieu operator (AMO), produced the first example of a fractal in physics known as “Hofstadter’s butterfly,” marking the starting point for the on-going strong interest in such operators in both mathematics and physics. Whereas research in the first three decades was focussed mainly on unraveling the unusual properties of the AMO , in recent years a combination of techniques from dynamical systems with those from spectral theory has allowed for a more “global,” model-independent point of view. Intriguing phenomena first encountered for the AMO , notably the appearance of a critical phase corresponding to purely singular continuous spectrum, could be tested for their prevalence in general models. This workshop will introduce the participants to some of the techniques necessary to understand the spectral properties of quasi-periodic Schrdinger operators. The presentation is of expository nature and will particularly emphasize the close ties to dynamical systems (``matrix cocycles’‘), which was successfully used to address several open problems (e.g. the ``Ten Martini problem’‘) and enabled above-mentioned global perspective. Topics included are: Basics: collectivity and regularity of spectral properties, matrix cocycles, arithmetic conditions Lyapunov exponent: positivity and continuity Supercritical behavior – Anderson localization Subcritical behavior – Duality, reducibility, and absolutely continuous spectrum Avila’s global theory and critical behavior 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 listsCambridge Neuroscience Seminar: New Approaches in Neuroscience MRC Cognition and Brain Sciences Unit Microsoft Research Computational Science Seminars## Other talksInterconversion of Light and Electricity in Molecular Semiconductors MEMS Particulate Sensors Simulating wave propagation in elastic systems using the Finite-Difference-Time-Domain method How archaeologists resolve the inductive risk argument Energy landscape of multivariate time series data Parkinson's Rehabilitation using interactive Dance Technology |