Franz Wegner: Topics

The introduction to some sections is not yet available.

Anderson Localization

Anderson localization is the localization of the eigenfunctions of particles and waves in a random potential. These may be electrons, but also phonons. Depending on the energy there may be localized and extended states. The energy separating these two types of states is called mobility edge.
In [
32] it is shown that the eigenstates in a linear chain with given boundary conditions can be considered as sum of states growing (exponentially) from both ends up to a certain lattice point, where they fulfill a matching condition. Summation is over all lattice points.
In [36,37] renormalization group arguments where applied to derive scaling laws for one- and two-particle correlations near the mobility edge. Two types of fixed point ensembles were introduced, the homogeneous one corresponding to the Wigner-Dyson classes, and the inhomogeneous one, realized in chiral and Bogolubov-de Gennes classes. They are checked against results obtained meanwhile [113].
In [38,39] disordered electronic systems were considered in a model of n orbitals at each lattice site, yielding first results on critical exponents in an ε expansion for dimension d=2+ε.
In [40,44] The mapping of the Anderson localization onto the non-linear σ model was derived. On this basis many calculations in 2+ε dimensions were performed.
The instanton concept was used in [46,47] to describe localized eigenstates and the a.c. conductivity in this regime.
Upper and lower bounds on the density of states were derived in [49].
An anomaly of the density of states in the band centre of the one-dimensional Anderson model was derived in [50].
The density of states for the lowest Landau Level in a weak white noise potential was calculated exactly in [53]. A two-subband lattice model was investigated in [80].
Calculations for the behaviour at the band centre of chiral models were given in [76].

Critical Phenomena

Renormalization Group in General

4-ε expansion

2+ε expansion

Tricriticality and three dimensions

Lattice Models, Duality

Critical Spin Dynamics and Anisotropy

Competing Order Parameters

Strongly Correlated Systems - Flow Equations

Flow equations for Hamiltonians transform Hamiltonians continuously into diagonal or block-diagonal form. Some applications are on electronic n-orbital models, elimination of the electron-phonon coupling, the Hubbard model and QED in the light front dynamics. Further information on
flow equations.

Floating Bodies of Equilibrium

Are there homogeneous bodies other than spheres (in three dimensions) and circles (in two dimensions) which can float in all orientations? Yes, such bodies exist. More on the
solution of the two-dimensional problem.


These contain
(i) my diploma thesis and a paper on the evaluation of Slater integrals,
(ii) some hierarchical models related to turbulent dynamics,
(iii) and a paper on rigid unit modes in tetrahedral crystals.

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