# Correlation Picture Approach to Open-Quantum-System Dynamics

## TL;DR

This paper introduces a correlation picture for open quantum systems, deriving an exact Lindblad-like dynamical equation that includes initial correlations, and develops a weak-correlation expansion for systematic approximations, improving over existing methods.

## Contribution

The paper presents a novel correlation picture framework that yields an exact open-system dynamics equation including initial correlations, along with a systematic perturbative expansion for practical approximations.

## Key findings

- Exact Lindblad-like equation with initial correlations derived
- Weak-correlation expansion formalism developed for approximations
- New Markovian master equation differing from existing approaches

## Abstract

We introduce a new dynamical picture, referred to as correlation picture,' which connects a correlated state to its uncorrelated counterpart. Using this picture allows us to derive an exact dynamical equation for a general open-system dynamics with system--environment correlations included. This exact dynamics is in the form of a Lindblad-like equation even in the presence of initial system-environment correlations. For explicit calculations, we also develop a weak-correlation expansion formalism that allows us to perform systematic perturbative approximations. This expansion provides approximate master equations which can feature advantages over existing weak-coupling techniques. As a special case, we derive a Markovian master equation, which is different from existing approaches. We compare our equations with corresponding standard weak-coupling equations by two examples, where our correlation picture formalism is more accurate, or at least as accurate as weak-coupling equations.