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

该项目旨在为高维混沌系统领域做出贡献，这些系统仍然对我们的理解构成许多挑战。在这里，新的合作现象，如相变，可以出现，这是不存在于系统的自由度少。为了模拟这样的功能，一类特殊的时空混沌系统，即耦合映射格子，已经证明是非常富有成效的。最近，一类映射格子已经被开发出来，它可以映射到一个随机自旋动力学的分析粗粒化过程中的微扰制度。我在博士学位期间研究了一维对称耦合链的应用论文，导致在一个平衡动力伊辛模型。新的功能，预计在空间二维系统，特别是不对称耦合，当相应的随机自旋动力学不服从详细的平衡引起真正的非平衡现象，如通过系统的能量通量。为了阐明非平衡相变，相应的主方程将从混沌动力学系统中导出，并将用动力学平均场和重整化群方法进行研究。通过这种方式，与Schmittmann教授和Zia教授的研究产生了许多联系，他们用类似的方法研究了不同的非平衡自旋模型。

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.