A weak-coupling master equation for arbitrary initial conditions

TL;DR

This paper derives a second-order weak-coupling master equation that describes the evolution of open quantum systems for any initial system-environment state, extending beyond the usual separable state assumption.

Contribution

It introduces a generalized master equation applicable to arbitrary initial states, providing conditions for Lindblad form recovery under common approximations.

Findings

Derived evolution equations valid for any initial state.

Identified conditions for Lindblad form emergence.

Extended applicability of master equations in open quantum systems.

Abstract

The structure of the initial system-environment state is fundamental to determining the nature and characteristics of the evolution of such an open quantum system. The usual assumption is to consider that the initial system-environment state is separable. Here, we go beyond this simple case and derive the evolution equations, up to second order in a weak-coupling expansion, that describe the evolution of the reduced density matrix of the system for any arbitrary system-environment initial state. The structure of these equations allows us to determine the initial conditions for which a Lindblad form can be recovered once applying the Markov and secular approximations.