We present a derivation of the Feynman–Vernon approach to open quantum systems in the language of super-operators. We show that this gives a new and more direct derivation of the generating function of energy changes in a bath, or baths. As found previously, this generating function is given by a Feynman–Vernon-like influence functional, with only time shifts in the kernels coupling the forward and backward paths. We further show that the new approach extends to an-harmonic and possible non-equilibrium baths, provided that the interactions are bi-linear, and that the baths do not interact between themselves. Such baths are characterized by non-trivial cumulants. Every non-zero cumulant of certain environment correlation functions is thus a kernel in a higher-order term in the Feynman–Vernon action.

中文翻译：

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费曼-弗农理论的算子推导，应用于浴能量变化的产生函数和非谐波浴

我们用超级算子的语言提出费曼-弗农方法对开放量子系统的推导。我们表明，这给出了一个浴池或多个浴池中能量变化的生成函数的新的更直接的推导。如前所述，此生成函数由类似Feynman-Vernon的影响函数给出，内核中只有时移耦合了前向和后向路径。我们进一步表明，只要相互作用是双线性的，并且浴之间不相互作用，则新方法可扩展到非谐波浴和可能的非平衡浴。这种浴的特征是非琐碎的累积物。因此，某些特定的环境相关函数的每个非零累积量在Feynman-Vernon动作中都是高阶项的内核。