Nonlinear Dynamics and Statistical Physics
We are primarily interested in the theory of nonlinear phenomena in magnetically ordered substances under strong nonequilibrium conditions. Taking ferromagnetic and antiferromagnetic materials on a mesoscopic or micromagnetic level, we investigate spatio-temporal mechanisms of pattern formation in externally driven magnets. We use the dissipative Landau-Lifshitz equation as the fundamental equation of motion. Our aim is to understand the complex global domain structures which are observed experimentally, as well as to study their basic ingredients such as domain walls, solitary states, fronts, etc.
We also approach the restricted class of problems consisting mainly of the occurrence of dynamical instabilities in an alternative manner. Starting off from first principles, i.e. from the microscopic quantum mechanical equations of motion, we then use quantum statistics. This provides an independent way of accessing these problems, as well as avoiding any sort of phenomenological assumptions.
In addition we compare our results with examples from hydrodynamics, nonlinear optics and chemistry, and in this manner define and clarify the position of magnetically ordered solids among these different pattern forming systems.