We aim at a theoretical description of collective and/or statistical properties of electrons in quantum matter. In the focus of our interest are quantum phase transitions, ordered quantum states and quantum transport phenomena. Our goal is to develop new methods to solve the quantum many body problem, to identify new physical concepts for the interpretation of experimental observations of current interest and to calculate observable properties.

At present the following projects are in progress:

- Theory of critical behaviour near a quantum phase transition in metallic heavy-fermion compounds (e.g. YbRh2Si2) including disorder.

(in collaboration with E. Abrahams, UC Los Angeles, USA; J. Schmalian, TKM) - Theory of electron transport in connected one-dimensional quantum wires within the Luttinger liquid model allowing a systematic determination of the fixed point structure and a direct calculation of the conductances and current fluctuations.

(in collaboration with D. Aristov, Nuclear Physics Institute, St. Petersburg, Russia; I. Gornyi, D. Polyakov, INT) - Analytical theory of the Kondo effect in the framework of functional renormalization theory. We generalize the „poor man’s scaling“ theory to strong coupling, taking into account the effect of spin relaxation. Our theory reproduces the known equilibrium properties. An extension to stationary nonequilibrium is in progress.

(in collaboration with J. Paaske, U Copenhagen, Denmark; H. Schmidt, formerly TKM) - Analytical theory of the scaling properties at the Anderson localisation transition of disordered electrons. We calculate the two-loop terms of the beta-function of the renormalization group equation of the frequency dependent conductivity in three dimensions. Our goal is a better determination of the critical exponents.

(in collaboration with K. Muttalib, T. Nakayama, U Florida, Gainesville, USA; P. Ostrovsky, TKM)