the vibrational modes of simplicial molecules

Published 2022

We consider simplicial molecules formed by placing identical point-masses at each vertex of a standard simplex and connecting them by identical springs. While the behavior of the molecule is well-known for two-atom, triangular, and tetrahedral molecules, we characterize the frequencies and modes for simplicial molecules of any dimension. 

Published: The Mathematical Intelligencer
View Paper: arXiv
Collaborators: Charles H. Conley

Quantum Intermittency for Sparse CMV Matrices with an Application to quantum walks on the half-line

Published 2016

We study the dynamics given by iteration of a CMV matrix with sparse, high barriers, and apply it to quantum walks on the half-line sparsely populated with strong reflectors.

Published: Journal of Approximation Theory
View Paper: arXiv
Collaborators: David Damanik, Jake Fillman, Gerhardt Hinkle, Alan Vu