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We apply the effective potential analytic continuation (EPAC) method to thecalculation of real time quantum correlation functions involving operatorsnonlinear in the position operator $\hat{q}$. For a harmonic system the EPACmethod provides the exact correlation function at all temperature ranges, whilethe other quantum dynamics methods, the centroid molecular dynamics and thering polymer molecular dynamics, become worse at lower temperature. For anasymmetric anharmonic system, the EPAC correlation function is in very goodagreement with the exact one at $t=0$. When the time increases from zero, theEPAC method gives good coincidence with the exact result at lower temperature.Finally, we propose a simplified version of the EPAC method to reduce thecomputational cost required for the calculation of the standard effectivepotential.Comment: REVTeX4, 18 pages, 9 eps figure

Effective potential analytic continuation approach for real time quantum correlation functions involving nonlinear operators