论文标题
完全阳性量子主方程的扰动稳态
Perturbative Steady States of Completely Positive Quantum Master Equations
论文作者
论文摘要
Lindblad形式保证了马尔可夫量子主方程（QME）的完全积极性。然而，它的微观衍生物用于量子系统与热浴的弱相互作用需要几个近似值，这可能会导致QME中的不准确性。最近，在不诉诸于红场方程的世俗近似的情况下得出了各种Lindbladian QME，这并不能保证完全阳性。在这里，我们以扰动的方式明确计算了这些Lindbladian QME的平衡稳态。我们将结果与从分析延续方法获得的红场方程的稳态进行了比较，后者与所谓的平均力吉布斯（MFG）状态相吻合。 MFG国家是通过整合吉布斯总汉密尔顿州吉布斯州的自由度而获得的。我们明确表明，林德布拉德QME的稳态与MFG状态不同。我们的结果表明，对QME的完全积极性所需的Redfield方程的操纵使其稳定状态远离MFG状态。我们还发现，在高温状态下，在某些条件下，Lindbladian QMES和MFG状态的稳态都降低到哈密顿量系统的同一吉布斯状态。
The Lindblad form guarantees complete positivity of a Markovian quantum master equation (QME). However, its microscopic derivation for a quantum system weakly interacting with a thermal bath requires several approximations, which may result in inaccuracies in the QME. Recently, various Lindbladian QMEs were derived without resorting to the secular approximation from the Redfield equation which does not guarantee the complete positivity. Here we explicitly calculate, in a perturbative manner, the equilibrium steady states of these Lindbladian QMEs. We compare the results with the steady state of the Redfield equation obtained from an analytic continuation method, which coincides with the so-called mean force Gibbs (MFG) state. The MFG state is obtained by integrating out the bath degrees of freedom for the Gibbs state of the total Hamiltonian. We explicitly show that the steady states of the Lindbladian QMEs are different from the MFG state. Our results indicate that manipulations of the Redfield equation needed to enforce complete positivity of a QME drives its steady state away from the MFG state. We also find that, in the high-temperature regime, both the steady states of the Lindbladian QMEs and MFG state reduce to the same Gibbs state of a system Hamiltonian under certain conditions.
