Iterative Monte Carlo with bead-adapted sampling for complex-time correlation functions

In a recent communication [V. Jadhao and N. Makri, J. Chem. Phys. 129, 161102 (2008)], we introduced an iterative Monte Carlo (IMC) path integral methodology for calculating complex-time correlation functions. This method constitutes a stepwise evaluation of the path integral on a grid selected by a Monte Carlo procedure, circumventing the exponential growth of statistical error with increasing propagation time, while realizing the advantageous scaling of importance sampling in the grid selection and integral evaluation. In the present paper, we present an improved formulation of IMC, which is based on a bead-adapted sampling procedure; thus leading to grid point distributions that closely resemble the absolute value of the integrand at each iteration. We show that the statistical error of IMC does not grow upon repeated iteration, in sharp contrast to the performance of the conventional path integral approach which leads to exponential increase in statistical uncertainty. Numerical results on systems with up to 13 degrees of freedom and propagation up to 30 times the “thermal” time $ℏβ/2$ illustrate these features.