Related Experiment Video
Updated: Sep 6, 2025

Measurement of the Directional Information Flow in fNIRS-Hyperscanning Data using the Partial Wavelet Transform Coherence Method
Published on: September 3, 2021
Application of the imaginary time hierarchical equations of motion method to calculate real time correlation
Tao Xing1, Tianchu Li1, Yaming Yan1
1Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China.
Abstract:
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.
Related Concept Videos
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Mean free path and Mean free time
Kinematic Equations - II
Suppose a car merges into freeway traffic on a 200 m long ramp. If its initial velocity is 10 m/s and it accelerates at 2 m/s2, then the...
Kinematic Equations - III
Using the kinematic equations,...
Impulse-Momentum Theorem
By writing Newton's second law of motion in terms of the momentum of an object and the external force acting on it, and simultaneously using the definition of the impulse vector, it can be shown that the total impulse on an object is equal to its...
Moment-of-Momentum Equation

