We all know that an isolated quantum system is governed by the Schodinger equation. However, in real world, a quantum system is always interacting with the surrounding (possibly macroscopic) environment. Such unavoidable interactions are an essential ingredient that contributes to the fact that we are living in a classical world.
Unfortunately, we typically are not able to follow the dynamics for the full system+environment considering the environment may consist of hundreds of degrees of freedom. In many cases, we are only interested in the primary system instead of the environment, we can focus on the reduced density matrix of the system only. The important question is then: How do we describe the evolution of the reduced density matrices?
In this manuscript, I introduce single Feynman diagrams and rules to directly write down the exact time-local master equation for a general open quantum system interacting with an arbitrary environment.