Abstract
It will be pointed out that there is a category of dynamic functions that is used and consequently understood commonly by all methodological communities, namely, temporal correlation functions. A correlation function terminology will be introduced as a sort of lingua franca of molecular dynamics. In a multidisciplinary, multi-methodological field such as soft-matter science, this is expected to facilitate communication among scientists employing different methods in studies of molecular dynamics. In the subsequent chapters, the reader will frequently be reminded of these “common denominators” of dynamic techniques. As further key concepts of pivotal importance, linear-response theory and the fluctuation-dissipation theorem will be outlined.
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Notes
- 1.
Molecular vibration and rotation states are excluded from detailed considerations here. Such excited molecular quantum states are subject of molecular spectroscopy of gases which is beyond the scope of this book.
- 2.
Note however that the magnetization grating generated in the course of such experiments is characterized by a modulation with a “wave” length corresponding to q. For an illustration, see Fig. 3.26.
- 3.
The static counterpart, that is, the static structure factor, is defined by \( S\left( {q} \right) = {{G}_{\mathrm{\rm coh}}}(0) \). Note also that the terminology “relative pair diffusion” often used in this context should be taken only cum grano salis since the double sums in Eq. (1.14) imply the cases \( j = l \), that is, self-diffusion.
- 4.
We use the calligraphic symbol \( { G}(t) \) throughout for normalized (or synonymously: reduced) correlation functions obeying the property \( { G}(0) = 1. \) Otherwise, Roman symbols like \( G(t) \) will be employed.
- 5.
Sometimes, the response function is also (and possibly misleadingly) called generalized susceptibility.
- 6.
Actually, quantum-mechanical diffraction of relatively large molecules has indeed been demonstrated as reported in Ref. [19]. However, it is not only the so-called decoherence that makes an influence on soft-matter dynamics unlikely. The conditions required for successful detection of diffraction of wave functions are far away from anything relevant for soft matter.
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Kimmich, R. (2012). Introduction. In: Principles of Soft-Matter Dynamics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5536-9_1
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