Quantification of memory effects in the spin-boson model

TL;DR

This paper systematically quantifies memory effects in the spin-boson model using a non-Markovianity measure, revealing regimes of strong non-Markovianity and conditions favoring Markovian dynamics.

Contribution

It applies a recent non-Markovianity measure to the spin-boson model without common approximations, identifying regimes of memory effects and explaining their origin.

Findings

Strong non-Markovianity at low temperatures and cutoffs

Existence of a regime favoring Markovian behavior due to resonance

Redfield equation reproduces key non-Markovian features

Abstract

Employing a recently proposed measure for quantum non-Markovianity, we carry out a systematic study of the size of memory effects in the spin-boson model for a large region of temperature and frequency cutoff parameters. The dynamics of the open system is described utilizing a second-order time-convolutionless master equation without the Markov or rotating wave approximations. While the dynamics is found to be strongly non-Markovian for low temperatures and cutoffs, in general, we observe a special regime favoring Markovian behavior. This effect is explained as resulting from a resonance between the system's transition frequency and the frequencies of the dominant environmental modes. We further demonstrate that the corresponding Redfield equation is capable of reproducing the characteristic features of the non-Markovian quantum behavior of the model.