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 Quantum transport
 Quantum dots
 Ultracold gases
 Strongly correlated systems
 Carbon nanotubes
 Flow equations for Hamiltonians
 Correlated fermions, Hubbard model
 Noise induced phenomena
 Anderson Localization
 Critical Phenomena and Renormalization Group
 Strongly Correlated Systems  Flow Equations
 Floating Bodies of Equilibrium
 Miscellenea
A.Komnik
A.Mielke
F.Wegner
Details
 Quantum transport ( A. Komnik)
During the recent decades it become feasible to manufacture semiconductor devices with sizes of 10100nm. At these scales quantum effects dominate almost all properties of such systems including their conductivity, a detailed knowledge of which is necessary to be able to design the circuitry of the future nanoelectronics. Quantum transport theory is trying to answer these questions.  Quantum dots ( A. Komnik)
Quantum dots represent the archetypical zerodimensional systems, which can be regarded as nanoscopic analogons of conventional transistors. It turns out that their properties are dominated by electronelectron interactions, which are responsible for such interesting phenomena as Coulomb blockade and Kondo effect. Current research concentrates on their nonlinear transport properties, transient phenomena taking place just after some of the parameters are abruptly changed as well as the charge and spin transfer statistics (aka full counting statistics) in the stationary state.  Ultracold gases ( A. Komnik)
The most remarkable fact about the ultracold gases is the possibility of manipulating their parameters in almost every possible way. Especially interesting is the availability of "taylored" interactions, which are almost impossible to realise with solid state setups. This makes ultracold gases to an ideal testing ground for investigations of strong correlation/interaction effects in condensed matter. We are working on different projects involving genuine BEC condensates in optical traps as well as ultracold Rydberg gases.  Strongly correlated systems ( A. Komnik)
Strongly correlated systems are responsible for a large number of intersting and not yet properly understood multiparticle phenomena such as hightemperature superconductivity and fractional quantum Hall effect. Despite an enormous progress in this fields during the last 20 years there is still an abyss of open problems. We are trying to apply the methods of bosonization, renormalisation group, conformal field theory as well as using integrability methods in order to understand the transport properties of such systems.  Carbon nanotubes ( A. Komnik)
The electronic degrees of freedom in carbon nanotubes are usually strongly correlated due to dimensional confinement to (quasi)1D geometry. In strictly 1D they are known to be adequately described by the universality class of TomonagaLuttinger liquids. Because of their extraordinary mechanical and electrical properties carbon nanotubes became one of the possible candidates for the basis material in nanoelectronics. We are conducting research aiming at understanding of their transport properties.
 Flow equations for Hamiltonians ( A. Mielke)
Using continuous unitary transformations one obtains flow equations for Hamiltonians. This new, nonperturbative 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 eight 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.
 Electronphonon coupling, superconductivity.
 Quantum mechanics of classically chaotic systems.
 Correlated fermions, Hubbard model
( A. Mielke)
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 flatband systems. They contain a flat band together with several dispersive bands. We have studied these models since 1991. An important point is the generalization of the results to models with a partially flat band. This is an important progress, since it opens a way to metallic ferromagnetism.
 Noise induced phenomena
( A. Mielke)
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 timecorrelated 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.
 Anderson Localization ( F. Wegner)
Anderson localization is the localization of the eigenfunctions of particles and waves in a random potential. Localized and extended states are separated by an energy, called mobility edge. The mapping of the mobility edge problem onto the nonlinear σmodel was introduced and investigated within 2+εexpansions. A general renormalization concept of the behaviour near the mobility edge was developped, distinguishing homogeneous fixedpoint ensembles (WignerDyson classes) and inhomogeneous ones (chiral and Bogolubovde Gennes classes). Upper and lower bounds on the density of states were given. List of Papers
 Critical Phenomena and Renormalization Group
( F.
Wegner)
The most recent work in this field was the investigation of an O(n)symmetric model of two nvector fields in D=42ε dimensions. Surprisingly two fixed points were found which agreed in order ε, but differed in order ε^{3/2}. Topics of other papers were renormalization in general, 4ε expansion, 2+ε expansion, lattice models and duality, tricriticality, critical spin dynamics and crossover in anisotropic systems. List of Papers
 Strongly Correlated Systems  Flow Equations
( F.
Wegner)
Continuous unitary transformations for Hamiltonians were introduced which bring Hamiltonians closer to diagonalization. Applications are on systems with twoparticle interaction (norbital model, Hubbard model) and to the elimination of the electronphonon interaction and others. List of papers More on Flow Equations
 Floating Bodies of Equilibrium
( F.
Wegner)
Homogeneous sufficiently convex bodies are considered, which can float in all orientations. An exact solution for the twodimensional problem has been given for densities different from 1/2. More on the twodimensional problem. Several results are obtained for the threedimensional problem. List of papers
 Miscellenea
( F.
Wegner)
The 'rigid unit mode' (RUM) models require unit blocks, in our case tetrahedra of SiO_{4} groups, to be rigid within first order of the displacements of the Oions. The wavevectors of the lattice vibrations, which obey this rigidity, were determined analytically. Generically lattices with inversion symmetry yield surfaces of RUMs in reciprocal space, whereas lattices without this symmetry yield generically lines of RUMs.
Earlier miscellaneous contributions were in anomalous diffusion on selfsimilar hierarchical structures and in nuclear physics. List of papers