Extending the applicability of Redfield theories into highly non-Markovian regimes

TL;DR

This paper introduces a computationally efficient hybrid method that extends Redfield theories to highly non-Markovian regimes by selectively propagating high-frequency bath modes and sampling low-frequency modes, significantly improving accuracy.

Contribution

The paper presents a novel hybrid approach combining Redfield equations with statistical sampling of low-frequency modes, enhancing applicability in non-Markovian regimes.

Findings

Improved Redfield dynamics in non-Markovian regimes

Comparable computational cost to traditional Redfield methods

Marginal benefit from classical evolution of low-frequency modes

Abstract

We present a new, computationally inexpensive method for the calculation of reduced density matrix dynamics for systems with a potentially large number of subsystem degrees of freedom coupled to a generic bath. The approach consists of propagation of weak-coupling Redfield-like equations for the high frequency bath degrees of freedom only, while the low frequency bath modes are dynamically arrested but statistically sampled. We examine the improvements afforded by this approximation by comparing with exact results for the spin-boson model over a wide range of parameter space. The results from the method are found to dramatically improve Redfield dynamics in highly non--Markovian regimes, at a similar computational cost. Relaxation of the mode-freezing approximation via classical (Ehrenfest) evolution of the low frequency modes results in a dynamical hybrid method. We find that this Redfield-based dynamical hybrid approach, which is computationally more expensive than bare Redfield dynamics, yields only a marginal improvement over the simpler approximation of complete mode arrest.