In 1981, Amir Caldeira and Anthony J. Leggett proposed a simplifying assumption in which the bath is decomposed to normal modes represented as harmonic oscillators linearly coupled to the system. As a result, the influence of the bath can be summarized by the bath spectral function. This method is known as the Caldeira–Leggett model, or harmonic bath model. To proceed and obtain explicit solutions, the path integral formulation description of quantum mechanics is typically employed. A large part of the power behind this method is the fact that harmonic oscillators are relatively well-understood compared to the true coupling that exists between the system and the bath. Unfortunately, while the Caldeira-Leggett model is one that leads to a physically consistent picture of quantum dissipation, its ergodic properties are too weak and so the dynamics of the model do not generate wide-scale quantum entanglement between the bath modes. An alternative bath model is a spin bath. At low temperatures and weak system-bath coupling, the Caldeira-Leggett and spin bath models are equivalent. But for higher temperatures or strong system-bath coupling, the spin bath model has strong ergodic properties. Once the system is coupled, significant entanglement is generated between all modes. In other words, the spin bath model can simulate the Caldeira-Leggett model, but the opposite is not true. An example of natural system being coupled to a spin bath is a nitrogen-vacancy (N-V) center in diamonds. In this example, the color center is the system and the bath consists of carbon-13 (13C) impurities which interact with the system via the magnetic dipole-dipole interaction. For open quantum systems where the bath has oscillations that are particularly fast, it is possible to average them out by looking at sufficiently large changes in time. This is possible because the average amplitude of fast oscillations over a large time scale is equal to the central value, which can always be chosen to be zero with a minor shift along the vertical axis. This method of simplifying problems is known as the secular approximation. Non-Markovian equations Open quantum systems that do not have the Markovian property are generally much more difficult to solve. This is largely due to the fact that the next state of a non-Markovian system is determined by each of its previous states, which rapidly increases the memory requirements to compute the evolution of the system. Currently, the methods of treating these systems employ what