The group is currently doing research in condensed matter theory, quantum quantum nonlinear dynamics (``quantum chaos''), and nonequilibrium systems. Below's a very brief exposure of our current research activities:
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nonlinear dynamics: we are applying path integral and field theoretical methods to understand universal phenomena in quantum systems that have a chaotic classical limit. Examples of such systems include ballistic semiconductor systems ('quantum billiards'), periodically driven systems, or weakly disordered electronic systems. At low energies, or large time scales, the physical properties of chaotic quantum systems become fully universal. In this regime, they can be modeled by phenomenological theories, such as random matrix theory. Why is this so? In recent years, we have been applying semiclassical and field theoretical concepts to understand the quantum-to-classical crossover in chaotic systems, and the origins of universality. The insights thus gained are now applied to address various applied problems in quantum chaos. |
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condensed matter theory: the group has been working on various types of condensed matter systems, notably systems influenced by the presence of static disorder. Examples include disordered metals and superconductors, interacting mesoscopic systems ('quantum dots'), and more exotic systems such as random magnetic field systems, graphene, anomalous superconductors, and others. How does the presence of static disorder affect the long range properties of electronic systems? And how will this change if interactions are present? What can be said about quantum interference phenomena and localization properties of unconventional systems such as superconductors, or systems with linear (relativistic) spectra? We have been working on these and related questions. |
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nonequilibrium systems: more recently, the focus of our research has shifted towards out of equilibrium phenomena, both classical and quantum. For example, we have studied how dynamically driven quantum systems (the Landau-Zener problem being the most elementary paradigm) evolve in the presence of interactions. We are also beginning to apply methodology that originates in quantum theory (such as the classical limits of Keldysh non-equilibrium techniques) to the study of large fluctuations in biological systems. Concrete problems include the analysis of fluctuations in compensatory mutations, and the role of fluctuations in autocatalytic RNA replication (unpublished). |
The work of the group is funded by SFB/TR 12 of the Deutsche Forschungsgemeinschaft. A list of recent publications can be found here.