Edwin Bernardoni with Rolfe Petschek
Optimization of the Static First Hyperpolarizibility of Many Non-Interacting Fermions
Large non-linear electronic polarizabilities would be advantageous for a variety of devices and have been intensely studied for around three decades. This project will examine theoretical limits on the static first non-linear electronic susceptibility of a material, β, known as the hyperpolarizability. Numerical optimizations for a single fermion in a one-dimensional potential strongly suggest that in this case the actual limit is about 70% of the analytically proven limit, and the same result obtains for multiple fermions when there is a strong attraction between them. We will investigate the results for non-interacting fermions, which seem a better model for actual electrons, which repel each-other, and expect a yet lower limit. Prior work in our group suggests in one dimension this ratio decreases with increasing number of non-interacting particles. We complete this work for segmented linear potentials, examine other model potentials specifically as finite sums of hermite polynomials and investigate the possibility that an analytic result can be obtained. Time permitting we will investigate the limits for multiple non-interacting electrons for the static second hyperpolarizability gamma.