Workshop on Dynamical Systems and Aperiodic Order
Bielefeld University, Germany
14th - 17th March 2011
All talks take place in Room V3-201 ("Common Room") in the Bielefeld
University main building.
Click here for
a description of the main building.
Dynamics of the Fibonacci trace map and some applications to
quasiperiodic models
William Yessen
Abstract:
Since the discovery of quasicrystals, quasiperiodic models in
mathematical physics have formed an active area of research. The
method of the so-called trace maps, originally introduced by
M. Kohmoto, L. P. Kadanoff and C. Tang in early '80s, has provided a means for
rigorous investigation into the physical properties of one-dimensional
quasiperiodic structures, leading, for example, to fundamental results
in the spectral theory of discrete Schrodinger operators and Ising
models (both classical and quantum) on one-dimensional quasiperiodic
lattices. We shall discuss dynamical properties of the so-called
Fibonacci trace map - an analytic map on the three-dimensional
Euclidean space that arises in the investigation of quasiperiodic
models on lattices generated by the Fibonacci substitution rule -
and its applications to the spectral theory of discrete quasiperiodic
Schrodinger operators and quasiperiodic Ising
models.
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