Markovian Master Equations: A Critical Study

TL;DR

This paper critically examines the derivation and validity of Markovian master equations for harmonic systems, comparing approximate dynamics with exact simulations to define their applicability and robustness.

Contribution

It provides a comprehensive analysis of Markovian master equations in various scenarios, including strong coupling, and assesses their accuracy against exact numerical results.

Findings

Markovian master equations are valid within specific regimes.

Approximate dynamics closely match exact simulations under certain conditions.

The methodology is broadly applicable to interacting chain systems with weak environmental coupling.

Abstract

We derive Markovian master equations of single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding Markovian master equations with exact numerical simulations of the evolution of the global system, we precisely delimit their validity regimes and assess the robustness of the assumptions usually made in the process of deriving the reduced dynamics. The proposed method is sufficiently general to suggest that the conclusions made here are widely applicable to a large class of settings involving interacting chains subject to a weak interaction with an environment.