CTMS Adventures In Theory Lectures
Tuesday, March 17, 2015, 4:30pm, 128 Physics
Michael I. Weinstein (Columbia University)
Energy on the edge - a mathematical view
Abstract:- Waves in free-space diffractively spread, while waves
in a spatially non-homogeneous medium undergo a combination of
scattering and localization.
In many applications, e.g. photonic and quantum systems, one is interested in
controlled localization of wave energy.
Edge states are a type of localization along a line-defect, the interface
between different media.
Topologically protected edge states are a class of edge states which are
robust to strong local distortions of the edge.
They are therefore potential vehicles for robust energy-transfer
in the presence of defects and random imperfections.
These states arise, for example, in graphene and its photonic analogues.
We first review the mathematics of dispersive waves in periodic media
and discuss examples of wave localization by a defect.
We then specialize to the case of honeycomb structures (such as grapheme)
and discuss their novel properties.
Finally we introduce and discuss a rich family of continuum partial differential equation
(Schroedinger) models, admitting edge states
which are topologically protected and those which are not.
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