Relaxation processes in supercooled liquids are known to exhibit interesting complex behavior. One of the hallmarks of this relaxation process observed in the measured auto correlation function is the occurrence of multiple steps of relaxations. The shorter time relaxation is known as the β-relaxation which is believed to be due to the motion of particles in the cage formed by their neighbors. The longer time relaxation is called the α-relaxation. The time scales of these two relaxations processes dramatically separate out with supercooling. In spite of decades of research, it is still not clearly known how these relaxation processes are related to each other. In this work, we show that there is a possible universal relation between short time β-relaxation and long time α-relaxation. We also show that the proposed relation can be rationalized within random first order transition theory of glass transition if power law relation is assumed between static and dynamic length scales.

中文翻译：

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玻璃形成液中短时间β弛豫和长时间α弛豫之间可能的普遍关系

已知在过冷液体中的松弛过程表现出令人感兴趣的复杂行为。在测得的自相关函数中观察到的这种松弛过程的标志之一是出现了多个松弛步骤。较短的时间弛豫被称为β松弛，这被认为是由于粒子在其邻居之间形成的笼子中的运动所致。较长的时间弛豫称为α松弛。这两个松弛过程的时间尺度通过过冷而明显地分开了。尽管进行了数十年的研究，但仍然不清楚这些松弛过程如何相互关联。在这项工作中，我们表明短时间β之间可能存在普遍关系。松弛和长时间的α松弛。我们还表明，如果假设静态和动态长度尺度之间的幂律关系，则可以在玻璃化转变的随机一阶转变理论中合理化建议的关系。