CRITICAL DYNAMICS

Reinhard Folk

Johannes Kepler University

An introduction into dynamical critical phenomena and their explanation will be given. Apart from a very short summary of the understanding of static critical behavior, in the first lecture we give an overview of the experimental situation in dynamics with concentration on liquids (transport coefficients, light scattering and sound), ferromagnets (neutron scattering) and the lambda transition in liquid helium-4 (thermal conductivity, second sound). We then discuss Van Hove theory and the concept of dynamic scaling theory. For a certain class of models the dynamical critcal exponent z can be found from applying this scaling concept below T_c. We end this part by introducing universality classes and its classification (models A-J). The second lecture contains technical points: We follow step by step the set up of the dynamical model for a liquid, and the transformations leading to a Lagrangian in order to match with static field theory. We discuss the perturbation theory and the structure of dynamical vertex functions, which have to be renormalized. The third lecture presents the comparion of the theoretical results with experiments. The main topic in this comparison will be the explanation of the observation as crossover phenomena: from background to asymptotics, from the hydrodynamic region to the critical region. This is demonstrated by temperature and wave vector dependence of the characteristic frequency in light scattering in liquids, and the frequency dependence of the shear viscosity, on the shape crossover of the scattering function in ferromagnets and the non asymptotic behavior of the thermal conductivity in He4 at the superfluid transition.

Text of the lecture (.pdf)

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