Effects of the rotating wave and secular approximations on non-Markovianity

TL;DR

This paper investigates how the rotating-wave and secular approximations affect the measurement of non-Markovianity in the spin-boson model, revealing that these approximations significantly underestimate non-Markovian effects.

Contribution

It provides a detailed analysis of the impact of RWA and SA on non-Markovianity and derives an accurate analytical expression without these approximations.

Findings

RWA and SA reduce observed non-Markovianity

Non-Markovianity persists over the entire relaxation time without approximations

An exact analytical expression for non-Markovianity is derived

Abstract

We study the effect of the rotating-wave approximation (RWA) and the secular approximation (SA) on the non-Markovian behavior in the spin-boson model at zero-temperature. We find that both the RWA and SA lead to a dramatic reduction in the observed non-Markovianity. In general, non-Markovian dynamics is observed for the whole relaxation time of the system, whereas the RWA and SA lead to such dynamics only on the short time scale of the environmental correlation time. Thus, the RWA and SA are not necessarily justified in the studies of non-Markovianity although they can estimate the state of the system precisely. Furthermore, we derive an accurate analytical expression for the non-Markovianity measure without the RWA or SA. This expression yields important insight into the physics of the problem.