Christopher Devulder - Hollow Shells of Dipoles: A Group Theoretical Approach

We use Group Theory to solve for the dipole interaction part of the Hamiltonian of various types of one (chain), two (ring) and three (cylinder) dimensional shells of dipoles. The fabrication of such structures has been recently achieved for various plasmonic devices, such as gold nanoparticles surrounding carbon nanotubes (1). These systems present various levels of rotational and translational symmetry that can be put in correspondence with symmetry groups and their matrix representations. This mapping of our physical system onto mathematical groups enables us to use several powerful results and theorems from linear algebra to diagonalize the interaction potential tensor that appears in the Hamiltonian. The resulting eigenmodes of oscillation can thus be obtained analytically with their corresponding energies.
Christopher Devulder is a graduating senior majoring in Physics who will be returning to  Lehigh for a 5th year in order to complete a second degree in  Mathematics. He has been working with Prof. Roktin for almost 2 years  on a plasmonic project that they hope to complete by the end of the  year. Devulder wishes to pursue further graduate studies in theoretical physics to study various unifying theories and their correlation to abstract mathematics.