Department of Physics, School of Science, Tianjin University, Tianjin 300072, China.
State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084, China.
Phys Rev E. 2023 Jan;107(1-1):014108. doi: 10.1103/PhysRevE.107.014108.
Master equations under appropriate assumptions are efficient tools for the study of open quantum systems. For many-body systems, subsystems of which locally couple to thermal baths and weakly interact with each other, the local approach provides a more convenient description than the global approach. However, these local master equations are believed to generate inconsistencies with the laws of thermodynamics when intersubsystem interactions exist. Here we develop an alternative local master equation by virtue of similar approximations used in deriving the traditional Gorini-Kossakowski-Lindblad-Sudarshan master equation. In particular, we stick to using eigenstates of each subsystem to construct quantum jump operators, and the secular approximation is also employed to modify the intersubsystem interactions. Our results show that violations of thermodynamic laws will be avoided after correcting intersubsystem interactions. Finally, we study a two-qubit heat transfer model and this further shows the validity of our modified master equation.
在适当的假设下，主方程是研究开放量子系统的有效工具。对于局部与热浴耦合并相互弱相互作用的多体系统，局部方法比全局方法提供了更方便的描述。然而，当存在子系统相互作用时，这些局部主方程被认为与热力学定律不一致。在这里，我们通过在推导传统的 Gorini-Kossakowski-Lindblad-Sudarshan 主方程中使用的类似近似方法来开发替代的局部主方程。特别地，我们坚持使用每个子系统的本征态来构建量子跳跃算子，并且还使用非时变近似来修改子系统间相互作用。我们的结果表明，在修正子系统间相互作用后，热力学定律的违反将被避免。最后，我们研究了一个两量子比特传热模型，这进一步表明了我们修正的主方程的有效性。
