A Comprehensive Approach to Finite-Bath Open Quantum Systems: Exact Dynamics

Abstract: Here, we develop the exact dynamics of the central spin model, modeling a finite-bath open quantum system. Particularly, two different types of interactions are investigated between the system and the bath: Heisenberg interaction with constant interaction strength, and a stochastic time-dependent interaction. In the former case, a new quantum channel is characterized, while the latter elucidates the microscopic understanding of a very well-known non-Markovian quantum channel. Exact master equations are provided in both scenarios. This is achieved by developing a new technique for obtaining a master equation from the map, making use of the concept of a minimal dissipator. This paves the way for a foundational understanding of finite-bath open quantum systems and a number of novel applications in the vast domain of quantum physics, one of which, implemented here, is in quantum thermodynamics.