Non-Markoffian effects of a simple nonlinear bath

TL;DR

This paper investigates the impact of a simple nonlinear, non-Markoffian bath on a spin system, comparing exact results with common approximation methods to understand the limitations of these approaches.

Contribution

It introduces a minimal model of a nonlinear bath and provides an exact analysis of its effects, highlighting discrepancies with standard approximation techniques.

Findings

Exact decay of spin correlator obtained

Markoffian and weak-coupling approximations compared

Linear bath substitution shows limitations

Abstract

We analyze a model of a nonlinear bath consisting of a single two-level system coupled to a linear bath (a classical noise force in the limit considered here). This allows us to study the effects of a nonlinear, non-Markoffian bath in a particularly simple situation. We analyze the effects of this bath onto the dynamics of a spin by calculating the decay of the equilibrium correlator of the spin's z-component. The exact results are compared with those obtained using three commonly used approximations: a Markoffian master equation for the spin dynamics, a weak-coupling approximation, and the substitution of a linear bath for the original nonlinear bath.