title: Partial averaging and the centroid virial estimator for stereographic projection path-integral simulations in curved spaces.
abstract: We develop and test three different partial averaging theories for the stereographic projection path integral in curved spaces. Additionally, we adapt and test the centroid virial estimator for the kinetic energy in curved spaces. We tested both a confining as well as a nonconfining potential for the particle in a ring. All three partial averaging theories are demonstrated to converge linearly in the asymptotic region with k(-2)max, the number of Fourier coefficients. We use an error estimator to determine the optimal parameters for an extrapolation to infinite kmax. We verify that the centroid virial estimator (derived from the primitive DeWitt path-integral formula) converges to the kinetic energy for both confining and nonconfining potentials.
authors.affiliation: Department of Chemistry and Physics, Arcadia University, Glenside, Pennsylvania 19038, USA.
authors.forename: Michael W
authors.initials: MW
authors.lastname: Avilés
authors.forename: E
authors.initials: E
authors.lastname: Curotto