Hierarchical theory of quantum dissipation: Partial fraction decomposition scheme

TL;DR

This paper introduces a partial fraction decomposition scheme for hierarchical equations of motion in bosonic quantum dissipation, significantly improving computational efficiency over traditional methods.

Contribution

It presents a novel partial fraction decomposition approach for hierarchical quantum dissipation theory, enhancing speed and efficiency for bosonic systems.

Findings

The new scheme is about ten times faster than conventional methods.

It effectively models spin-boson systems with improved performance.

The approach applies similar properties as the Fermi function expansion.

Abstract

We propose a partial fraction decomposition scheme to the construction of hierarchical equations of motion theory for bosonic quantum dissipation systems. The expansion of Bose--Einstein function in this scheme shows similar properties as it applies for Fermi function. The performance of the resulting quantum dissipation theory is exemplified with spin--boson systems. In all cases we have tested the new theory performs much better, about an order of magnitude faster, than the best available conventional theory based on Matsubara spectral decomposition scheme.