论文标题
Hu-Paz-Zhang主方程的适用范围
Range of applicability of the Hu-Paz-Zhang master equation
论文作者
论文摘要
我们研究了Caldeira-Leggett模型的Hu-Paz-Zhang Master方程的情况，而没有在弱耦合极限之前获得的lindblad形式，直到二阶扰动。在我们的研究中，我们使用高斯初始状态能够采用足够且必要的条件，这可以在时间演化期间暴露对密度算子的阳性侵犯。我们证明，当固定解决方案不是积极的操作员，即没有物理解释时，非马克维亚主方程的演变存在问题。我们还表明，解决方案始终保持物理，以进行小时的进化。此外，当解决方案的痕迹分歧时，我们确定了强烈的反常行为。我们还为相应的马尔可夫主方程提供了结果，并表明即使固定解决方案是正算子，对于各种类型的初始条件也会发生阳性违规行为。根据我们的数值结果，我们得出结论，这个非马克维亚主方程优于相应的马尔可夫。
We investigate a case of the Hu-Paz-Zhang master equation of the Caldeira-Leggett model without Lindblad form obtained in the weak-coupling limit up to the second-order perturbation. In our study, we use Gaussian initial states to be able to employ a sufficient and necessary condition, which can expose positivity violations of the density operator during the time evolution. We demonstrate that the evolution of the non-Markovian master equation has problems when the stationary solution is not a positive operator, i.e., does not have physical interpretation. We also show that solutions always remain physical for small-times of evolution. Moreover, we identify a strong anomalous behavior, when the trace of the solution is diverging. We also provide results for the corresponding Markovian master equation and show that positivity violations occur for various types of initial conditions even when the stationary solution is a positive operator. Based on our numerical results, we conclude that this non-Markovian master equation is superior to the corresponding Markovian one.
