Using continuous unitary transformations one obtains flow equations for Hamiltonians. This new, non-perturbative method can be used to diagonalize or renormalize a given Hamiltonian. The method is useful for problems with different energy scales or strong interactions. The method has been developed 25 years ago by Franz Wegner for problems of many particle physics and independently by Stan Glazek and Kenneth Wilson for bound state problems in QCD. Since that time we use this method to treat various kinds of problems including

• Dissipative quantum systems
• Electron-phonon coupling, superconductivity
• Quantum mechanics of classically chaotic systems

One of our main interest for the future is to study correlated electron systems using this method. We expect that the method can be applied successfully to such problems, since it directly renormalizes the Hamiltonian and therefore allows the description of bound states or correlated states.

Ferromagnetism in the Hubbard model has been investigated for long time. Unfortunately, only few exact results are available. A class of models where we were able to proof the existence and the uniqueness of ferromagnetic ground states are the so called flat-band systems. They contain a flat band together with several dispersive bands.

We have studied these models since 1991. In the last two years we were able to generalize some of the results to models with a partially flat band. This is an important progresss, since it opens a way to metallic ferromagnetism.

Interacting bosons in flat band structures show various interesting effects including the formation of a Wigner crystal and pair formation.

The interaction of a small classical system with its environment can often be described by a stochastic force. A thermal environment is usually described by a white noise. Models that contain time-correlated noise or a white noise and some additional periodic forces show interesting new phenomena. Typical examples are stochastic resonance, noise induced transport, and noise induced stability. We obtained some interesting results for the last two classes of systems. Most of these models are motivated by biological systems like motor proteins or cell surface receptors.

In he following areas I offer Bachelor's and Master's theses:

• Hubbard model, strong correlations. The main interest here is to study systems with a flat band, esp. in three dimensions. Requirements: Students should have interest in mathematical physics. A course in advanced condensed matter theory may be helpful.
• Stochastic systems. Here we study some special models, esp. from biological physics, mainly using analytical methods. Requirements: Courses in quantum mechansics and statistical physics.