A method for calculating time correlation functions

Hermann Haken, Wolfgang Weidlich

G. Yue

Dave Thirumalai, B. J. Berne

A Monte Carlo method for calculating quantum mechanical time correlation functions is presented. In this method the time correlation function is calculated at several values along the pure imaginary axis of the complex time plane such that 0<it<β, where (β)−1 is the temperature of the system. Using the periodicity of the imaginary time correlation function, the real time behavior is inferred by analytic continuation. The method is used to calculate the absorption spectra of two model systems.

Peter Millington

A. Karpati, Петер Адам, József Janszky

We developed a technique for calculating two-time correlation functions based on a quantum trajectory approach. Our method requires the simulation of the evolution of a given set of density matrices only once. The evaluation can be carried out from the density matrix data obtained for any quantities, time arguments and initial conditions. The computational efficiency of the method is estimated and an example of application is presented.

Tao Xing, Tianchu Li, Yaming Yan +2 more

We investigate the application of the imaginary time hierarchical equations of motion method to calculate real time quantum correlation functions. By starting from the path integral expression for the correlated system-bath equilibrium state, we first derive a new set of equations that decouple the imaginary time propagation and the calculation of auxiliary density operators. The new equations, thus, greatly simplify the calculation of the equilibrium correlated initial state that is subsequently used in the real time propagation to obtain the quantum correlation functions. It is also shown that a periodic decomposition of the bath imaginary time correlation function is no longer necessary in the new equations such that different decomposition schemes can be explored. The applicability of the new method is demonstrated in several numerical examples, including the spin-Boson model, the Holstein model, and the double-well model for proton transfer reaction.