In this article we investigate driven dissipative quantum dynamics of an ensemble of two-level systems given by a Markovian master equation with collective and local dissipators. Exploiting the permutation symmetry in our model, we employ a phase space approach for the solution of this equation in terms of a diagonal representation with respect to certain generalized spin coherent states. Remarkably, this allows to interpolate between mean field theory and finite system size in a formalism independent of Hilbert-space dimension. Moreover, in certain parameter regimes, the evolution equation for the corresponding quasiprobability distribution resembles a Fokker–Planck equation, which can be efficiently solved by stochastic calculus. Then, the dynamics can be seen as classical in the sense that no entanglement between the two-level systems is generated. Our results expose, utilize and promote techniques pioneered in the context of laser theory, which can be powerful tools to investigate problems of current theoretical and experimental interest.

在本文中，我们研究了由具有集体和局部耗散体的马尔可夫主方程给出的两级系统整体的驱动耗散量子动力学。在我们的模型中利用置换对称性，我们针对特定的广义自旋相干态采用对角表示形式，采用相空间方法求解该方程。值得注意的是，这允许在独立于希尔伯特空间维的形式主义中的均值场理论和有限系统大小之间进行插值。此外，在某些参数范围内，对应拟概率分布的演化方程类似于Fokker-Planck方程，可以通过随机演算有效地求解。然后，从两层系统之间不产生纠缠的意义上讲，动力学可以看作是经典的。我们的研究结果揭示，利用和推广了在激光理论的背景下开创的技术，这些技术可以成为研究当前理论和实验问题的有力工具。