THEORY OF CONDENSED MATTER
General Scientific Goals
The topics of research in the Theory of Condensed Matter group are stochasticity and disorder as well as structure formation in soft condensed matter and solids, models of complex biological systems, strongly correlated electron systems, and superconducting materials. Investigations using modern analytic methods and computer applications complement and stimulate each other. Research is performed in cooperation with mathematicians as well as with theoretical and experimental physicists, biologists and researchers in medicine. There are well established collaborations with research groups in France, Germany, Italy, Russia, Switzerland, UK, and USA.
Noise induced phenomena (Behn) are studied in a number of different systems. Structure formation, stochastic stability, and on-off intermittency is investigated in liquid crystals driven by stochastic electric fields. Noise induced non-equilibrium phase transitions are studied in coupled arrays of stochastically driven nonlinear systems. The statistics of first passage times and self-organized criticality is investigated in stochastic nonlinear systems with time delay.
Mathematical modeling of the immune system (Behn). Using methods of nonlinear dynamics and statistical physics, we study the architecture and the random evolution of the idiotypic network of the B-cell subsystem and describe the regulation of balance of Th1/Th2-cell subsystems, its relation to allergy and the hyposensitization therapy (Cooperation with the Institute for Clinical Immunology and Transfusion Medicine).
Strongly correlated electron systems (Ihle). The unconventional magnetic properties of transition metal oxides, such as the mixed-valency manganites,are investigated on the basis of correlation models including anisotropic Heisenberg-type exchange interactions. Using Green's function techniques the effects of magnetic short-range order at arbitrary temperatures are studied in comparison with experiments.
Non-equilibrium dynamics of various soft-condensed-matter systems (Kroy). The latter range from desert dunes spontaneously developing as a generic consequence of aeolian sand transport, through non-equilibrium gels of adhesive colloids and proteins, the viscoelastic mechanics of the cytoskeleton, to the non-equilibrium dynamics of single DNA molecules under strong external fields. (Related experimental work is currently in progress at EXP1: PWM, PAF.) A common feature is the presence of strong fluctuations and stochastic dynamics on the micro-scale. The emergence of macroscopic structure and (non-linear) deterministic macroscopic dynamics is to be understood. The applied methods range from analytical studies of stochastic integro-differential equations through liquid-state theories, mode-coupling theory, effective hydrodynamic equations, phenomenological modeling, to numerical simulations.