Path integral centroid theories for the simulation of condensed-phase quantum dynamics

Equilibrium quantum dynamical processes in condensed phase can be studied in terms of path integral centroid and relevant objects. There are two existing theories, one being the path integral quantum transition state theory (PI-QTST), a quantum activated reaction rate theory, and the other being the centroid molecular dynamics (CMD) method, which enables the calculation of equilibrium time correlation functions. These theories are suitable for applications to quantum condensed matter systems, but their theoretical bases have not been well understood. A rigorous theory is presented where dynamical path integral centroid variables can be defined and related to the time evolution of equilibrium ensemble. The CMD method is understood within this formalism, and alternative approximations are also found. Then, the same formalism is applied to the process of quantum activated reaction where it is found that the PI-QTST is closely related to the CMD approximation and can be improved further. Finally, a new path integral simulation algorithm is presented which helps make the CMD simulation more efficient.