Multiple relaxation channels often arise in the dynamics of liquids where the momentum current associated to the particle-conservation law splits into distinct contributions. Examples are strongly confined liquids for which the currents in lateral and longitudinal direction to the walls are very different, or fluids of nonspherical particles with distinct relaxation patterns for translational and rotational degrees of freedom. Here, we perform an asymptotic analysis of the slow structural relaxation close to kinetic arrest as described by mode-coupling theory (MCT) with several relaxation channels. Compared to standard MCT, the presence of multiple relaxation channels significantly changes the structure of the underlying equations of motion and leads to additional, non-trivial terms in the asymptotic solution. We show that the solution can be rescaled, and thus prove that the well-known $ \beta $-scaling equation of MCT remains valid even in the presence of multiple relaxation channels. The asymptotic treatment is validated using a novel schematic model. We demonstrate that the numerical solution of this schematic model can indeed be described by the derived asymptotic scaling laws close to kinetic arrest. Additionally, clear traces of the existence of two distinct decay channels are found in the low-frequency susceptibility spectrum, suggesting that clear footprints of the additional relaxation channels can in principle be detected in simulations or experiments of confined or molecular liquids.

中文翻译：

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具有多个衰减通道的模式耦合理论的标度方程

多个弛豫通道经常出现在液体动力学中，其中与粒子守恒定律相关的动量流分裂成不同的贡献。例子是强约束液体，其横向和纵向到壁的电流非常不同，或者非球形粒子的流体具有不同的平移和旋转自由度弛豫模式。在这里，我们对接近动力学停滞的缓慢结构弛豫进行渐近分析，如模式耦合理论 (MCT) 所描述的，具有多个弛豫通道。与标准 MCT 相比，多个弛豫通道的存在显着改变了基本运动方程的结构，并在渐近解中产生了额外的、非平凡的项。我们表明该解决方案可以重新缩放，从而证明即使在存在多个松弛通道的情况下，众所周知的 MCT 的 $\beta $-scaling 方程仍然有效。使用新的示意图模型验证渐近处理。我们证明了这个示意图模型的数值解确实可以通过接近动力学停滞的导出渐近标度定律来描述。此外，在低频磁化率谱中发现了存在两个不同衰减通道的清晰痕迹，这表明原则上可以在受限或分子液体的模拟或实验中检测到额外弛豫通道的清晰足迹。使用新的示意图模型验证渐近处理。我们证明了这个示意图模型的数值解确实可以通过接近动力学停滞的导出渐近标度定律来描述。此外，在低频磁化率谱中发现了存在两个不同衰减通道的清晰痕迹，这表明原则上可以在受限或分子液体的模拟或实验中检测到额外弛豫通道的清晰足迹。使用新的示意图模型验证渐近处理。我们证明了这个示意图模型的数值解确实可以通过接近动力学停滞的导出渐近标度定律来描述。此外，在低频磁化率谱中发现了存在两个不同衰减通道的清晰痕迹，这表明原则上可以在受限或分子液体的模拟或实验中检测到额外弛豫通道的清晰足迹。