Complex quantum systems exhibit phenomena of coherent quantum mechanics often combined with statistical properties and classical chaos. Prominent exponents are mesoscopic systems building a bridge between microscopic objects such as atoms and macroscopic, traditional condensed matter systems. Charge transport through quantum systems of mesoscopic to molecular scales – in particular, ballistic nanostructures, quantum dots, graphene and single molecules – is the focus of our research.

In the context of semiconductor-based spin-electronics, we are interested in spin effects in coherent charge transport under the influence of inhomogeneous magnetic fields or spin-orbit interactions. The coupling of orbital and spin degrees of freedom, combined with effects due to the finite system geometry, leads to novel effects in spin dynamics and relaxation: recently, we have demonstrated that the combination of a periodic potential and spin-orbit interactions in mesoscopic conductors with AC voltage provides spin-polarized currents, thus acting as a ”spin ratchet”.

Transport physics in graphene nanostructures has moved into focus of our research. Besides the treatment of the system boundary effects we are particularly interested in spin effects in graphene.

We also investigate the charge transport through single-molecule bridges between macroscopic conductors to learn how genuine molecular properties, such as vibrational degrees of freedom of the molecules, as well as interaction effects (Coulomb blockade), modify the conductance of molecular bridges. Our quantum transport calculations are carried out mostly in the context of the Landauer and Keldysh formalism with the aid of Green function methods.

Mesoscopic systems in the intermediate regime between micro- and macrophysics are ideal candidates for studying the interplay between classical and quantum mechanics; in particular, signatures of chaotic classical dynamics in the corresponding quantum system. By developing advanced semiclassical methods we managed to detect subtle correlations in classical dynamics which proved to be of key importance for the explanation of statistical properties of energy levels, as well as allow a consistent formulation of a semiclassical theory of the ballistic quantum transport.

At the gateway between atomic and mesoscopic physics we investigate the propagation of Bose-Einstein condensates through artificial atomic wave guides and cavities (“atom on a chip”). Nonlinearities in the equations describing the condensate dynamics lead to specific effects; for example, the “atom blockade” in the transmission through double-barriers, which was discovered by our group.