标题： 结构化开放量子系统的部分久期近似和统一主方程的数值实现 显示英文标题

标题： Numerical implementation of the partial secular approximation and unified master equation in structured open quantum systems

摘要： 开放量子系统的马尔可夫动力学通常通过林德布洛德方程来描述，这些方程是通过完整的主项近似从雷德菲尔德方程导出的。后者忽略了主方程中与不同玻尔频率的跃迁算符对相对应的旋转项。然而，对于许多物理系统，这种近似失效，因此需要更精确地处理缓慢旋转的项。实际上，通过进行部分主项近似可以得到更精确的物理结果，该近似考虑了每对跃迁算符相关的相关时间尺度，并将其与系统-环境耦合产生的时间尺度进行比较。在本工作中，我们引入了一个通用代码，用于在结构化开放量子系统的雷德菲尔德方程中进行部分主项近似。该代码可以应用于任何多体系统与玻色浴耦合的通用哈密顿量。此外，它还可以再现统一主方程，该方程在部分主项近似下捕捉到与雷德菲尔德方程相同的物理行为，但数学上保证生成一个完全正的动态映射。最后，该代码可以计算同一物理问题的局部和全局版本的主方程。我们通过研究由两个耦合到玻色模式的超导量子比特组成的结构化开放量子系统的稳态热流来说明该代码。本工作中的结果可用于数值研究广泛范围的复杂开放量子系统。 显示英文摘要

摘要： The Markovian dynamics of open quantum systems is typically described through Lindblad equations, which are derived from the Redfield equation via the full secular approximation. The latter neglects the rotating terms in the master equation corresponding to pairs of jump operators with different Bohr frequencies. However, for many physical systems this approximation breaks down, and thus a more accurate treatment of the slowly rotating terms is required. Indeed, more precise physical results can be obtained by performing the partial secular approximation, which takes into account the relevant time scale associated with each pair of jump operators and compares it with the time scale arising from the system-environment coupling. In this work, we introduce a general code for performing the partial secular approximation in the Redfield equation for structured open quantum systems. The code can be applied to a generic Hamiltonian of any multipartite system coupled to bosonic baths. Moreover, it can also reproduce the unified master equation, which captures the same physical behavior as the Redfield equation under the partial secular approximation, but is mathematically guaranteed to generate a completely positive dynamical map. Finally, the code can compute both the local and global version of the master equation for the same physical problem. We illustrate the code by studying the steady-state heat flow in a structured open quantum system composed of two superconducting qubits, each coupled to a bosonic mode, which in turn interacts with a thermal bath. The results in this work can be employed for the numerical study of a wide range of complex open quantum systems.