Equations of structural relaxation

In the mode coupling theory of the liquid to glass transition the long time structural relaxation follows from equations solely determined by equilibrium structural parameters. The present extension of these structural relaxation equations to arbitrarily short times on the one hand allows calculations unaffected by model assumptions about the microscopic dynamics and on the other hand supplies new starting points for analytical studies. As a first application, power-law like structural relaxation at a glass-transition singularity is explicitly proven for a special schematic MCT model.Comment: 11 pages, 3 figures; talk given at the Seventh international Workshop on disordered Systems, Molveno, Italy, March 199

Localization, anomalous diffusion and slow relaxations: a random distance matrix approach

We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such as the diffusion of particles, slow relaxations in glasses, and scalar phonon localization. Using a combination of a renormalization group procedure and a direct moment calculation, we find the eigenvalue distribution density (i.e., the spectrum) and the localization properties of the eigenmodes, for arbitrary dimension. Finally, we discuss the physical implications of the results

The field inside a random distribution of parallel dipoles

We determine the probability distribution for the field inside a random uniform distribution of electric or magnetic dipoles. For parallel dipoles, simulations and an analytical derivation show that although the average contribution from any spherical shell around the probe position vanishes, the Levy stable distribution of the field is symmetric around a non-vanishing field amplitude. In addition we show how omission of contributions from a small volume around the probe leads to a field distribution with a vanishing mean, which, in the limit of vanishing excluded volume, converges to the shifted distribution.Comment: RevTeX, 4 pages, 3 figures. Submitted to Phys. Rev. Let

Constitutional and Congressional Requirements Directing Public Lands Decisionmaking

15 pages. Contains references