Spin-boson dynamics beyond conventional perturbation theories

TL;DR

This paper introduces the Weakly-Interacting Blip Approximation (WIBA), a nonperturbative method for accurately modeling spin-boson dynamics across various regimes, surpassing traditional perturbative approaches.

Contribution

The paper presents WIBA, a novel approximation scheme that accurately describes spin-boson dynamics beyond conventional perturbation theories, valid over wide temperature and coupling ranges.

Findings

WIBA agrees with perturbative methods in their respective limits.

WIBA provides reliable results across a broad parameter space.

The approach is based on a path-integral and generalized master equation framework.

Abstract

A novel approximation scheme is proposed to describe the dynamics of the spin-boson problem. Being nonperturbative in the coupling strength nor in the tunneling frequency, it gives reliable results over a wide regime of temperatures and coupling strength to the thermal environment for a large class of bath spectral densities. We use a path-integral approach and start from the exact solution for the two-level system population difference in the form of a generalized master equation (GME). Then, we approximate inter-blip and blip-sojourns interactions up to linear order, while retaining all intra-blip correlations to find the kernels entering the GME in analytical form. Our approximation scheme, which we call Weakly-Interacting Blip Approximation (WIBA), fully agrees with conventional perturbative approximations in the tunneling matrix element (Non-Interacting Blip Approximation) or in the system-bath coupling strength.