By exploiting the peculiarities of a recently introduced formalism for describing open quantum systems (the parametric representation with environmental coherent states) we derive an equation of motion for the reduced density operator of an open quantum system that has the same structure of the celebrated Gorini–Kossakowski–Sudarshan–Lindblad equation, but holds regardless of Markovianity being assumed. The operators in our result have explicit expressions in terms of the Hamiltonian describing the interactions with the environment, and can be computed once a specific model is considered. We find that, instead of a single set of Lindblad operators, in the general (non-Markovian) case there one set of Lindblad-like operators for each and every point of a symplectic manifold associated to the environment. This intricacy disappears under some assumptions (which are related to Markovianity and the classical limit of the environment), under which it is possible to recover the usual master-equation formalism. Finally, we find such Lindblad-like operators for two different models of a qubit in a bosonic environment, and show that in the classical limit of the environment their renown master equations are recovered.

通过利用最近引入的描述开放量子系统的形式主义的特性（具有环境相干状态的参数表示），我们推导出了开放量子系统的降低密度算子的运动方程，该系统具有与著名的 Gorini-Kossakowski 相同的结构–Sudarshan–Lindblad 方程，但无论假设马尔可夫性如何都成立。我们结果中的算子在描述与环境交互的哈密顿量方面具有明确的表达式，并且可以在考虑特定模型后进行计算。我们发现，在一般（非马尔可夫）情况下，对于与环境相关的辛流形的每个点，都有一组类似 Lindblad 的算子，而不是一组 Lindblad 算子。这种复杂性在一些假设（与马尔可夫性和环境的经典极限有关）下消失了，在这些假设下，可以恢复通常的主方程形式主义。最后，我们在玻色子环境中为两个不同的量子比特模型找到了类似 Lindblad 的算子，并表明在环境的经典极限下，它们著名的主方程得到了恢复。