Collective bath coordinate mapping of "hierarchy" in hierarchical equations of motion
Abstract
The theory of hierarchical equations of motion (HEOM) is one of the standard methods to give exact evaluations of the dynamics as coupled to harmonic oscillator environments. However, the theory is numerically demanding due to its hierarchy, which is the set of auxiliary elements introduced to capture the nonMarkovian and nonperturbative effects of environments. When systembath coupling becomes relatively strong, the required computational resources and precision move beyond the regime that can be currently handled. This article presents a new representation of HEOM theory in which the hierarchy is mapped into a continuous space of a collective bath coordinate and several auxiliary coordinates as the form of the quantum FokkerPlanck equation. This representation gives a rigorous time evolution of the bath coordinate distribution and is more stable and efficient than the original HEOM theory, particularly when there is a strong systembath coupling. We demonstrate the suitability of this approach to treat vibronic system models coupled to environments.
 Publication:

Journal of Chemical Physics
 Pub Date:
 March 2022
 DOI:
 10.1063/5.0082936
 arXiv:
 arXiv:2112.09861
 Bibcode:
 2022JChPh.156j4104I
 Keywords:

 Physics  Chemical Physics;
 Condensed Matter  Statistical Mechanics;
 Quantum Physics
 EPrint:
 18 pages, 5 figures