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MP: Theoretische und Mathematische Grundlagen der Physik

MP II: HV II

MP II.1: Invited Talk

Monday, March 26, 2001, 17:15–18:15, HS VIII

From Many Interacting Particles to Collective Few-Body Modes: Motion of Shocks in Driven Diffusive Systems — •Guntes M. Schütz — Forschungszentrum Jülich, Institut für Festkörperphysik

Questions arising frequently in the description of many-body systems concern the mechanism of emergence of a small number of effective degrees of freedom (characterizing the macroscopic state of the system) from the collective behaviour a large number of dynamical modes on a more microscopic level. The q-deformed symmetries of integrable quantum spin chains are shown to provide a tool for the rigorous derivation of n-body dynamics for n interacting shocks in the 1-d asymmetric exclusion process, a simple lattice model for biased diffusive motion of infinitely many hard-core particles. The time evolution of shock measures can be calculated explicitly on the lattice scale using the Bethe ansatz. This model provides a rare instance where the coarse-graining involved in the passing from microscopic to macroscopic scales can be performed exactly on all intermediate scales and thus allows for conjectures concerning stability criteria for shocks in more general driven diffusive systems.