中文摘要：

基于拓展的热库统计准粒子代数法，构建了二次型环境耦合的耗散子方程组新理论．为验证耗散子代数中新增法则的正确性，采用完全不同的方法推导了扩展Zusman方程，并证明新理论在Zusman方程相同的预设条件下，正是后者的动力学解．由此证实当增加一对耗散子时，推广（非高斯）Wick定理的正确性，这一新法则使得耗散子方法可以很自然拓展到非线性环境耦合．此外，还需注意并必须加以考虑的是：与线性耦合不同，非高斯环境的影响不能完全通过线性响应理论来描述，它的影响在所发展的耗散子方程组理论中体现于耗散子和非线性热库作用描述符之间的相互耦合，文中对此进行了着重的阐述．最后模拟和展示了二次型环境耦合下的吸收光谱线型．

英文摘要：

In this work we construct a novel dissipaton-equation-of-motion （DEOM） theory in quadratic bath coupling environment, based on an extended algebraic statistical quasi-particle approach. To validate the new ingredient of the underlying dissipaton algebra, we derive an extended Zusman equation via a totally different approach. We prove that the new theory, if it starts with the identical setup, constitutes the dynamical resolutions to the extended Zusman equation. Thus, we verify the generalized （non-Gaussian） Wick＇s theorem with dissipatons-pair added. This new algebraic ingredient enables the dissipaton approach being naturally extended to nonlinear coupling environments. Moreover, it is noticed that, unlike the linear bath coupling case, the influence of a non-Gaussian environment cannot be completely characterized with the linear response theory. The new theory has to take this fact into account. The developed DEOM theory manifests the dynamical interplay between dissipatons and nonlinear bath coupling descriptors that will be specified. Numerical demonstrations will be given with the optical line shapes in quadratic coupling environment.