Quantum Chaos and Elastic Shells
Advantages of shells are their lightness and on the conceptual side the
dimensional reduction from three to two. The equations of a shell are
given by a high order partial differential system describing the
three-dimensional displacement field as a function of the position on a
two-dimensional surface. Nevertheless, shell theory is the simplest
effective theory of curved elastic two-dimensional objects. Besides
domes, cars, aero-planes and bells, shell theory has also been applied to
fullerenes and carbon nanotubes.
The analogue of quantum billiards in elasticity are resonators.
If the underlying space is curved some results for the spectrum are known
in the quantum case. In the curved elastic case, the situation then
becomes that of shells. In general, it is expected that semiclassical
methods from quantum chaos will provide an understanding of high frequency
vibrations of shells.
The talk shall give an overview of shells, their classical ray limit and
discuss the upcoming experiments at the Niels Bohr Institute by Clive
Ellegaard and Mikkel Avlund. Further collaborators are Thomas Guhr (LTH)
and Mark Oxborrow (NPL,UK).