  We introduce mapping-variable ring polymer molecular dynamics (MV-RPMD), a
model dynamics for the direct simulation of multi-electron processes. An
extension of the RPMD idea, this method is based on an exact, imaginary time
path-integral representation of the quantum Boltzmann operator using continuous
Cartesian variables for both electronic states and nuclear degrees of freedom.
We demonstrate the accuracy of the MV-RPMD approach in calculations of
real-time, thermal correlation functions for a range of two-state single-mode
model systems with different coupling strengths and asymmetries. Further, we
show that the ensemble of classical trajectories employed in these simulations
preserves the Boltzmann distribution and provides a direct probe into real-time
coupling between electronic state transitions and nuclear dynamics.
