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arXiv 1906.02583quant-ph
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微扰主方程的精度评估--包含非正性

Accuracy Assessment of Perturbative Master Equations -- Embracing Non-Positivity

Richard Hartmann, Walter T. Strunz

备注：
minor changes for reasons of a consistent notation
发表信息：
Phys. Rev. A 101, 012103 (2020)
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摘要：

从微观哈密顿量得到的开放量子系统的约化动力学一般只能用时间局域主方程近似描述。这种近似的质量主要取决于耦合强度和环境结构。各种这样的主方程已经提出了不同的目的。为特定系统选择最合适的系统并不简单。通过专注于减少动力学的准确性，我们提供了一个彻底的评估方法（Redfield方程，量子光学主方程，粗粒主方程，相关的动态映射方法和部分长期近似）的选择。在这里，我们认为一种方法是否能保证积极性是次要的。我们使用两个量子位耦合到一个洛伦兹环境中的自旋玻色子一样的时尚建模与各种系统和浴时间尺度的一般情况。我们看到，与初始状态无关，具有时间相关系数的简单Redfield方程比所考虑的所有其他方法都要精确得多。我们强调，积极违反Redfield形式主义成为相关的制度，这里考虑的任何微扰主方程是无效的。这意味着积极性的丧失实际上应该作为一个重要的功能：受到欢迎：它表明弱耦合假设的崩溃。此外，我们提出了各种方法，在一个独立的方式，并使用他们的错误的行为，以提供进一步的洞察到每种方法的有效性范围。

英文摘要：

The reduced dynamics of an open quantum system obtained from an underlying microscopic Hamiltonian can in general only approximately be described by a time local master equation. The quality of that approximation depends primarily on the coupling strength and the structure of the environment. Various such master equations have been proposed with different aims. Choosing the most suitable one for a specific system is not straight forward. By focusing on the accuracy of the reduced dynamics we provide a thorough assessment for a selection of methods (Redfield Equation, Quantum Optical Master Equation, Coarse-Grained Master Equation, a related dynamical map approach and a partial-secular approximation). Whether or not an approach guarantees positivity we consider secondary, here. We use two qubits coupled to a Lorentzian environment in a spin-boson like fashion modeling a generic situation with various system and bath time scales. We see that, independent of the initial state, the simple Redfield Equation with time dependent coefficients is significantly more accurate than all other methods under consideration. We emphasize that positivity violation in the Redfield formalism becomes relevant only in a regime where any of the perturbative master equations considered here are rendered invalid anyway. This implies that the loss of positivity should in fact be welcomed as an important feature: it indicates the breakdown of the weak coupling assumption. In addition we present the various approaches in a self-contained way and use the behavior of their errors to provide further insight into the range of validity of each method.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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