Quantum Chaos and Elastic Shells

Niels Søndergaard

Abstract: 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).