Spectral theory of the Schr?dinger operators on fractals

Add to your list(s) Download to your calendar using vCal

• Molchanov, S (University of North Carolina)
• Thursday 25 June 2015, 10:00-11:00
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact webseminars.

Periodic and Ergodic Spectral Problems

Spectral theory of the Schr?dinger operators on fractals (Stanislav Molchanov UNC Charlotte)

Spectral properties of the Laplacian on the fractals as well as related topics (random walks on the fractal lattices, Brownian motion on the Sierpinski gasket etc.) are well understood. The next natural step is the analysis of the corresponding Schr?dinger operators and not only with random ergodic potentials (Anderson type Hamiltonians) but also with the classical potentials: fast decreasing, increasing or periodic (in an appropriate sense) ones. The talk will present several results in this direction. They include a) Simon Spencer type theorem (on the absence of a.c. spectrum) and localization theorem for the fractal nested lattices (Sierpinski lattice) b) Homogenization theorem for the random walks with the periodic intensities of the jumps c) Quasi-classical asymptotics and Bargman type estimates for the Schr?dinger operator with the decreasing gasket d) Bohr asymptotic formula in the case of the increasing to infinity potentials e) Random hierarchical operators, density of states and the non-Poissonian spectral statistics Some parts of the talk are based on joint research with my collaborators (Yu. Godin, A. Gordon, E. Ray, L. Zheng).

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.