Information content of multitime correlation functions for the interpretation of structural relaxation in glass-forming systems
Information content of multitime correlation functions for the interpretation of structural relaxation in glass-forming systems
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用于解释玻璃形成系统中结构松弛的多时间相关函数的信息内容
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发表时间：
1997
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通讯作者：
A. Heuer
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作者：
A. Heuer
在最近的实验中，通过多维NMR方法系统地测量了玻璃化转变附近聚合物的四时间相关函数[A. Heuer等人，物理修订信函75，2851（1995）]。本文从理论上分析了多时间相关函数的信息量。考虑到弛豫速率的异质分布，它表明，多时间相关函数包含有关的异质分布内的时间波动的信息。如果弛豫速率分布是双峰的，则与两次相关函数相比，四次相关函数的附加信息内容由两个动力学状态之间的交换速率给出。更一般地，对于任意速率分布，多时间相关函数的附加信息内容可以很好地近似由单个无量纲参数$Q$表示。该参数是非均匀分布内波动的度量。它表示为速率记忆参数。有人认为，它的价值是有关的协同动力学。
In recent experiments four-time correlation functions have been systematically measured for a polymer near the glass transition via methods of multidimensional NMR [A. Heuer et al., Phys. Rev. Lett. 75, 2851 (1995)]. In this paper a theoretical analysis of the information content of multitime correlation functions is presented. Having in mind a heterogeneous distribution of relaxation rates, it is demonstrated that multitime correlation functions contain information about temporal fluctuations within the heterogenous distribution. If the relaxation rate distribution is bimodal, the additional information content of the four-time correlation function as compared to the two-time correlation function is given by the exchange rate between both dynamical states. More generally, for arbitrary rate distributions the additional information content of multitime correlation functions can be, to a good approximation, expressed by a single dimensionless parameter $Q$. This parameter is a measure for the fluctuations within the heterogeneous distribution. It is denoted rate memory parameter. It is argued that its value is related to the cooperativity of the dynamics.