A generalized viscoelastic quantum hydrodynamic model is proposed for the dynamics of strongly correlated degenerate isothermal fluid. The quantum forces associated with the quantum diffraction effect along with the strong correlation effects are embedded in this transport equation through the viscoelastic relaxation of correlations. The collective dynamics of linear and nonlinear modes in such correlated degenerate fluid are also investigated. In the high-frequency oscillation (kinetic regime), the dynamics of the weakly nonlinear mode is found to be governed by a novel equation with a memory dependent non-local nonlinear term that describes the strong correlation effect. This novel equation is solved analytically and numerically. In the low-frequency oscillation (hydrodynamic regime), the weakly nonlinear mode is found to be governed by a Korteweg–de Vries Burgers' equation that exhibits dispersive shock wave. In both the dynamics, quantum diffraction introduces the dispersive effect.

针对强相关简并等温流体的动力学，提出了一种广义的粘弹性量子流体力学模型。通过相关的粘弹性松弛，将与量子衍射效应以及强相关效应相关的量子力嵌入此传输方程中。还研究了在这种相关的退化流体中线性和非线性模式的集体动力学。在高频振荡（动力学状态）中，发现弱非线性模式的动力学受一个新方程式的控制，该方程式具有描述强相关效应的与记忆有关的非局部非线性项。这个新的方程是通过解析和数值求解的。在低频振荡（流体动力态），发现弱非线性模式由表现出分散冲击波的Korteweg-de Vries Burgers方程控制。在这两种动力学中，量子衍射都会引入色散效应。