Kooperative Phänomene in raum-zeitlichen chaotischen Modellen und ihre Beziehung zu Nichtgleichgewichtsphasenübergängen

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The project intends to contribute to the field of high dimensional chaotic systems which still pose many challenges to our understanding. Here new cooperative phenomena like phase transitions can emerge, which are not present in systems with few degrees of freedom. To model such features a particular class of spatio-temporal chaotic systems, namely coupled map lattices, have turned out to be very fruitful. Recently, a class of map lattices has been developed which can be mapped to a stochastic spin dynamics by an analytical coarse graining procedure in a perturbative regime. An application to a one dimensional symmetrically coupled chain was worked out in my Ph.D. thesis, resulting in an equilibrium kinetic Ising model. Novel features are expected in spatially two dimensional systems and in particular for asymmetric couplings, when the corresponding stochastic spin dynamics does not obey detailed balance giving rise to genuine non-equilibrium phenomena like energy fluxes through the system. In order to shed some light on non-equilibrium phase transitions the corresponding master equation will be derived from the chaotic dynamical system and will be studied with dynamical mean field and renormalization group approaches. In this way many connections to the research of Prof. Schmittmann and Prof. Zia arise who have studied diverse nonequilibrium spin models with similar methods.