The Regularized Resolvent Transform for Quantum Dynamics Calculations,

Abstract

A recently introduced numerical expression for spectral estimation, called the regularized resolvent transform (RRT) (J. Magn. Reson. 2000, 147, 129), is shown to be very useful in a number of applications in quantum dynamics calculations. RRT has emerged from the filter diagonalization method (FDM), although it is based on a different linear algebraic algorithm and, therefore, has different numerical properties, such as stability, robustness, speed, etc. Given a time signal c(t), RRT provides a direct estimate of its infinite time Fourier spectrum I(s). Replacement of the argument s in the RRT expression by −iE leads to a very useful formula to estimate the inverse Laplace transform of c(t). Two applications of RRT are discussed in detail: the calculation of all S-matrix elements using a single wave packet propagation and the problem of estimating the microcanonical quantities, such as the density of states, from the canonical cross-correlation functions.