Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 7: Statistical physics II (general)

DY 7.2: Talk

Tuesday, March 24, 2009, 10:00–10:15, HÜL 386

Green-Kubo formalism for solids — •Henk van Beijeren — Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht, The Netherlands — Zentrum Mathematik, Bereich M5 Technische Universität München D-85747 Garching bei München (bis Juli 2009), Germany

The Green-Kubo formalism yields macroscopic transport equations on the basis of the microscopic equations of motion, by postulating the existence of a set of slowly varying microscopic phase functions, whose dynamics allow for a closed macroscopic description. These functions always include the long-wavelength Fourier components of energy, momentum and mass densities. In systems with broken symmetries the order parameters describing these have to be added. In solids these primarily are displacement fields, describing the displacements of the atoms from their equilibrium positions. The resulting macroscopic equations are the elastic equations describing propagation and damping of sound and Fourier's law of heat conduction. The Green-Kubo formalism expresses the transport coefficients and damping constants occurring in these equations in terms of time integrals of current-current time correlation functions.

I will present the general structure of these equations together with the Green-Kubo expressions for transport and damping coefficients. If time allows I will consider mode-coupling predictions for the long time behavior of the correlation functions relevant for heat diffusion. I will discuss divergences of transport coefficients and their finite-size renormalization.