  This paper reviews the linearized path integral approach for computing time
dependent properties of systems that can be approximated using a mixed
quantum-classical description. This approach is applied to studying vibrational
pure dephasing of ground state molecular iodine in a rare gas matrix. The
Feynman-Kleinert optimized harmonic approximation for the full system density
operator is used to sample initial conditions for the bath degrees of freedom.
This extremely efficient approach is compared with alternative initial
condition sampling techniques at low temperatures where classical initial
condition sampling yields dephasing rates that are nearly an order of magnitude
too slow compared with quantum initial condition sampling and experimental
results.
