S-matrix network models for coherent waves in random media: construction and renormalization

Networks of random quantum scatterers (S-matrices) form paradigmatic models for the propagation of coherent waves in random S-matrix network models cover universal localization-delocalization properties and have some advantages over more traditional Hamiltonian models. In particular, a straightforward implementation of real space renormalization techniques is possible. Starting from a finite elementary cell of the S-matrix network, hierarchical network models can be constructed by recursion. The localization-delocalization properties are contained in the flow of the forward scattering strength ('conductance') under increasing system size. With the aid of 'small scale' numerics qualitative aspects of the localization-delocalization properties of S-matrix network models can be worked out.Comment: 10 pages, LaTeX, 8 eps figures included, proceedings PILS98, to be published in Annalen der Physi

Multifractality beyond the Parabolic Approximation: Deviations from the Log-normal Distribution at Criticality in Quantum Hall Systems

Based on differences of generalized R\'enyi entropies nontrivial constraints on the shape of the distribution function of broadly distributed observables are derived introducing a new parameter in order to quantify the deviation from lognormality. As a test example the properties of the two--measure random Cantor set are calculated exactly and finally using the results of numerical simulations the distribution of the eigenvector components calculated in the critical region of the lowest Landau--band is analyzed.Comment: LaTeX 4 pages, 3 EPS included, to appear in Europhysics Letter

Economic Impacts of Post-CRP Policy Options in South Dakota

Agricultural and Food Policy,

Lattice Electrons on a Cylinder Surface in the Presence of Rational Magnetic Flux and Disorder

We consider a disordered two-dimensional system of independent lattice electrons in a perpendicular magnetic field with rigid confinement in one direction and generalized periodic boundary conditions (GPBC) in the other direction. The objects investigated numerically are the orbits in the plane spanned by the energy eigenvalues and the corresponding center of mass coordinate in the confined direction, parameterized by the phase characterizing the GPBC. The Kubo Hall conductivity is expressed in terms of the winding numbers of these orbits. For vanishing disorder the spectrum of the system consists of Harper bands with energy levels corresponding to the edge states within the band gaps. Disorder leads to broadening of the bands. For sufficiently large systems localized states occur in the band tails. We find that within the mobility gaps of bulk states the Diophantine equation determines the value of the Hall conductivity as known for systems with torus geometry (PBCs in both directions). Within the spectral bands of extended states the Hall conductivity fluctuates strongly. For sufficiently large systems the generic behavior of localization-delocalization transitions characteristic for the quantum Hall effect are recovered.Comment: RevTeX, 10 pages, 14 PostScript figure

Assessing farmer behaviour as affected by policy and technological innovations: bio-economic farm models

Farm Management,