From Kinetic Models to Hydrodynamics by Matteo Colangeli

Author:Matteo Colangeli
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

where is the entropy change of the system due to the macroscopic fluctuation. It can thus be shown [2] that in the hydrodynamic regime, attains the form

(4.28)

Thus, consists of three components: the Rayleigh line centered at , and the two Brillouin lines, located at ; cf. the left panel of Fig. 4.1. As mentioned in Sect. 4.1, the power spectrum constitutes an important source of information for experimentalists. The measure of the Brillouin–Rayleigh spectrum by light scattering in a simple liquid makes it possible, in fact, to compute the speed of sound (from the position of the Brillouin peaks) as well as the lifetime of the thermal fluctuations and that of the sound waves (from the knowledge of and respectively). A further characterization of the hydrodynamic regime can be obtained by looking at the self part of the van Hove function. It is possible to show [1, 9] that in the limit of small wave vectors and low frequencies, behaves as if the tagged particle were undergoing a diffusive process. The evolution equation is hence of the form

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