Application of the imaginary time hierarchical equations of motion method to calculate real time correlation functions
- 22 June 2022
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 156 (24), 244102
- https://doi.org/10.1063/5.0095790
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.Funding Information
- National Natural Science Foundation of China (21933011)
- K. C. Wong Education Foundation
This publication has 51 references indexed in Scilit:
- Filtered propagator functional for iterative dynamics of quantum dissipative systemsComputer Physics Communications, 1997
- A novel method for simulating quantum dissipative systemsThe Journal of Chemical Physics, 1996
- Quasi-adiabatic propagator path integral methods. Exact quantum rate constants for condensed phase reactionsChemical Physics Letters, 1993
- Quantum and classical Fokker-Planck equations for a Gaussian-Markovian noise bathPhysical Review A, 1991
- Dynamics of the dissipative two-state systemReviews of Modern Physics, 1987
- Path integral approach to quantum Brownian motionPhysica A: Statistical Mechanics and its Applications, 1983
- Quantum mechanical transition state theory and a new semiclassical model for reaction rate constantsThe Journal of Chemical Physics, 1974
- The theory of a general quantum system interacting with a linear dissipative systemAnnals of Physics, 1963
- Studies of polaron motion: Part II. The “small” polaronAnnals of Physics, 1959
- Studies of polaron motion: Part I. The molecular-crystal modelAnnals of Physics, 1959