  We propose a new quantum dynamics method called the effective potential
analytic continuation (EPAC) to calculate the real time quantum correlation
functions at finite temperature. The method is based on the effective action
formalism which includes the standard effective potential. The basic notions of
the EPAC are presented for a one-dimensional double well system in comparison
with the centroid molecular dynamics (CMD) and the exact real time quantum
correlation function. It is shown that both the EPAC and the CMD well reproduce
the exact short time behavior, while at longer time their results deviate from
the exact one. The CMD correlation function damps rapidly with time because of
ensemble dephasing. The EPAC correlation function, however, can reproduce the
long time oscillation inherent in the quantum double well systems. It is also
shown that the EPAC correlation function can be improved toward the exact
correlation function by means of the higher order derivative expansion of the
effective action.
