Dr. Manny Curotto, Professor and Chair of Chemistry and Physics, and Sarah E. Wolf, a junior Chemistry major who has been doing research with Curotto for two years,presented their work on “Ring Polymer Dynamics in Curved Spaces” at the 244th American Chemical Society National Meeting and Exposition: Materials for Health and Medicine, held in Philadelphia, Aug. 19-23.
They propose a new algorithm for the integration of the Ring Polymer Hamiltonian in curved spaces designed to improve the stability of the state of the art symplectic integrators based on the split - operator approach was proposed. The theory was tested by simulating the particle in a ring T1 mapped by a stereographic projection using three potentials. Two of these are quadratic, and one is a nonconfining sinusoidal model. For manifolds, the position - position autocorrelation function can be formulated in numerous ways. The position - position autocorrelation function computed from configurations in the Euclidean space R2, that contains T1 as a submanifold, has the best statistical properties. The agreement with exact results obtained with vector space methods is excellent for all three potentials, for all values of time in the interval simulated, and for a relatively broad range of temperatures.