Response functions as quantifiers of non-Markovianity

TL;DR

This paper introduces a linear response-based method to quantify non-Markovianity in quantum systems with initially correlated states, simplifying analysis and revealing non-Markovian effects in classical and quantum models.

Contribution

It presents a novel approach using response functions to derive dynamical maps for correlated states, enabling easier quantification of non-Markovianity.

Findings

Non-Markovian behavior can occur in classical Brownian particles with initial correlations.

The proposed quantifier is valid beyond linear response in the Caldeira-Leggett model.

No simple relation exists between the quantifier and system-bath coupling parameters.

Abstract

Quantum non-Markovianity is crucially related to the study of dynamical maps, which are usually derived for initially factorized system-bath states. We here demonstrate that linear response theory also provides a way to derive dynamical maps, but for initially correlated (and in general entangled) states. Importantly, these maps are always time-translational invariant and allow for a much simpler quantification of non-Markovianity compared to previous approaches. We apply our theory to the Caldeira-Leggett model, for which our quantifier is valid beyond linear response and can be expressed analytically. We find that a classical Brownian particle coupled to an Ohmic bath can already exhibit non-Markovian behaviour, a phenomenon related to the initial state preparation procedure. Furthermore, for a peaked spectral density we demonstrate that there is no monotonic relation between our quantifier and the system-bath coupling strength, the sharpness of the peak or the resonance frequency in the bath.