4. Conclusions
The HEOM approach is now
available in the modular open-source Libra software, starting from the
version v4.8.1. This version is available at the Zenodo
server42 as well as from the Quantum Dynamics Hub
GitHub Libra software repository
https://github.com/Quantum-Dynamics-Hub/libra-code. The current
work provides a comprehensive account on the underlying theoretical
foundations and terminology of the method, the key algorithms used, and
the important implementation details and use guidance. The detailed
examples to run the calculations presented in this work are available at
the Zenodo server43 as well as from the GitHub data
repository https://github.com/AkimovLab/Project_HEOM.
The present implementation features a user-friendly design of the
Python-level modules for HEOM calculation, which shall facilitate the
use of this method in Jupyter- or Python-based calculations. Our current
implementation considers a number of acceleration features, such as
using the scaled HEOM method, filtering the HEOM, using the concept of
active equation lists, which are updated periodically to remove the
propagation of ADMs when the ADM’s time derivatives are negligible. A
nearly trivial OpenMP parallelization is incorporated in the step of
computing ADM’s time-derivatives and leads to expected acceleration of
the computations. We have provided examples of using the code for
propagating reduced density matrices to describe quantum dynamics of
open systems. We have illustrated the capabilities of the present HEOM
implementation in computing spectral line shapes. We have provided a
number of examples on the expected qualitative changes in the dynamics
of quantum systems in response to variation of various properties of the
bath. We have provided some computational scalability and execution time
benchmarks to guide the potential users of this software in feasibility
of various types of calculations.