Analysis of memory effects in the dynamic evolution of the spin-boson model

TL;DR

This paper investigates non-Markovian effects in the spin-boson model at strong couplings by transforming the Hamiltonian to a polaron frame, revealing effective non-Markovian dynamics within certain coupling ranges.

Contribution

It introduces a perturbative approach using polaron transformation to analyze memory effects in the spin-boson model at strong coupling regimes.

Findings

Non-Markovian effects are present within specific coupling ranges.

Correlation timescales are shorter than relaxation times in the transformed frame.

Effective non-Markovian behavior emerges under large polaron theory.

Abstract

Quantum information processing relies on how dynamics unfold in open quantum systems. In this work, we study the non-Markovian dynamics in the single mode spin-boson model at strong couplings. In order to apply perturbation theory, we transform our Hamiltonian to polaron frame, so that the effective system-bath coupling gets reduced. We employ coherence defined by l1-norm to analyze the non-Markovian effects in the spin-boson model. In the transformed frame of reference, the correlation timescales for the bath are significantly shorter than the system's relaxation timescale-a key assumption for Markovian dynamics. However, intriguingly, we demonstrate that under the large polaron theory, the reduced dynamics exhibit effective non-Markovian behaviour within a specific range of couplings, while remaining Markovian beyond this range.