Simulating Non-Markovian Dynamics in Open Quantum Systems

TL;DR

This paper reviews and unifies various simulation methods for non-Markovian open quantum system dynamics, providing a comprehensive framework that clarifies their relationships, strengths, and limitations to advance the field.

Contribution

It introduces a unified framework linking different simulation approaches, enhancing understanding and facilitating progress in modeling non-Markovian quantum dynamics.

Findings

Provides a systematic overview of existing methods.

Links different approaches within a unified framework.

Clarifies physical interpretations and applicability of methods.

Abstract

Recent advances in quantum technologies and related experiments have created a need for highly accurate, versatile, and computationally efficient simulation techniques for the dynamics of open quantum systems. Long-lived correlation effects (non-Markovianity), system-environment hybridization, and the necessity for accuracy beyond the Born-Markov approximation form particular challenges. Approaches to meet these challenges have been introduced, originating from different fields, such as hierarchical equations of motion, Lindblad-pseudomode formulas, chain-mapping approaches, quantum Brownian motion master equations, stochastic unravelings, and refined quantum master equations. This diversity, while indicative of the field's relevance, has inadvertently led to a fragmentation that hinders cohesive advances and their effective cross-community application to current problems for complex systems. How are different approaches related to each other? What are their strengths and limitations? Here we give a systematic overview and concise discussion addressing these questions. We make use of a unified framework which very conveniently allows to link different schemes and, this way, may also catalyze further progress. In line with the state of the art, this framework is formulated not in a fully reduced space of the system but in an extended state space which in a minimal fashion includes effective reservoir modes. This in turn offers a comprehensive understanding of existing methods, elucidating their physical interpretations, interconnections, and applicability.