Long time behavior of correlation functions: connections between system and measured quantities

Abstract

In the present paper an approach concerning the formalism of time dependent Pair Correlation Functions (PCF), which characterize the time-space properties of material systems and their Fourier Transforms (FT) is presented. In particular, the effects of the system-probe interaction are dealt by taking into account the coupling between the system properties, through the PCF, and the instrument response function, through its resolution function. Such an approach shows the effects of the instrumental resolution function on the time dependent PCF and on its FT. It emerges that the system dynamics that occurs on a time scale longer than the instrumental energy resolution, is entirely summed up in the elastic contribution whereas the system dynamics on a time scale shorter than the instrumental energy resolution is weighted by the resolution function. As a consequence, by changing the instrumental resolution one can register a crossover between a condition dominated by the elastic contribution to a condition dominated by the quasi-elastic contribution; this occurs when the system relaxation time matches the instrumental resolution time. This procedure reveals to be useful for the analysis of elastic and quasi-elastic signals.