Optimized hierarchical equations of motion for Drude dissipation

TL;DR

This paper presents an optimized hierarchical equations of motion approach for Drude dissipation, introducing a convergence criterion and employing a Padé spectrum decomposition, validated through quantum system benchmarks.

Contribution

It introduces an optimized hierarchical EOM method with a new convergence criterion based on Padé spectrum decomposition for efficient quantum dissipation modeling.

Findings

Effective convergence criterion for hierarchical EOMs

Accurate modeling of spin-boson and exciton systems

Validated approach with benchmark comparisons

Abstract

The hierarchical equations of motion theory for Drude dissipation is optimized, with a convenient convergence criterion proposed in advance of numerical propagations. The theoretical construction is on basis of a Pad\'{e} spectrum decomposition that has been qualified to be the best sum-over-poles scheme for quantum distribution function. The resulting hierarchical dynamics under the {\em apriori} convergence criterion are exemplified with a benchmark spin-boson system, and also the transient absorption and two-dimensional spectroscopy of a model exciton dimer system.