Ring Polymer Dynamics (RPD) is an approach for approximating the quantum dynamics of a system by using the hamiltonian of a fictitious ring polymer. When working in curved spaces, such as those created with the introduction of holonomic constraints, the presence of a non-uniform metric alters the ring polymer dynamics, and causes difficulties manifested in significant long-time energy drift, which should be absent in a good algorithm used when the hamiltonian is constant with respect to time translations. Using an integrator developed with the aid of the variational principle, we apply RPD to curved spaces, specifically testing a symmetric ellipsoid of inertia mapped in stereographic projection coordinates. We find that the algorithm conserves the energy (without long-term energy drift) and that the relative energy difference decreases with the square of the time step. We graph the position-position autocorrelation function over time, using Cartesian coordinates, at several values of the Trotter number.

Variational integrator for ring polymer dynamics in curved spaces

247th National Meeting (2014)

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