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Projekt P5


Fluctuation and Response Behaviour at Phase Transitions in Driven Lattice Gases and Brownian Motors


Philipp Maass


Phase transitions, like the condensation of a gas into liquid, are well-known phenomena in our daily life. Their occurrence and properties can be understood theoretically from equilibrium statistical mechanics. Between steady states in non-equilibrium, which carry permanent currents, similar phase transitions occur. They are found even in one-dimensional systems with short-range particle interactions, where phase transitions between equilibrium states are absent. While the foundations of equilibrium statistical mechanics were developed more than a century ago, our understanding of non-equilibrium system is still comparatively limited due to the difficulties to state general, overarching principles for these systems. This project shall contribute to to the continuing efforts for improving this situation. Its goal is to gain a deeper understanding of non-equilibrium phase transitions by analytical and simulation studies of driven lattice gases. Such lattice gases constitute suitable models for basic investigations of non-equilibrium dynamics and phase transitions. At the same time they find numerous applications for describing transport processes, as, for example, directed motions of motor proteins inside of cells. Certain mathematical treatments of driven lattice gases moreover show a close connection to quantum-mechanical calculations of interacting spin systems. In our modelling, short-range particle interactions are taken into account beyond simple exclusion interactions, which were considered in most of the previous studies. The focus of the research will be on the analysis of fluctuation properties of physical quantities near phase transitions between non-equilibrium steady states and their response behaviour with respect to external perturbations. This includes also investigations of phase transitions between stationary states of periodically driven systems known as Brownian motors.