Diffusion and Velocity Auto-Correlation in Shearing Granular Media

We perform numerical simulations to examine particle diffusion at steady shear in a model granular material in two dimensions at the jamming density and zero temperature. We confirm findings by others that the diffusion constant depends on shear rate as $D\sim\dot\gamma^{q_D}$ with $q_D<1$, and set out to determine a relation between $q_D$ and other exponents that characterize the jamming transition. We then examine the the velocity auto-correlation function, note that it is governed by two processes with different time scales, and identify a new fundamental exponent, $\lambda$, that characterizes an algebraic decay of correlations with time

Fine Tuning in Supersymmetric Models

The solution of a fine tuning problem is one of the principal motivations of Supersymmetry. However experimental constraints indicate that many Supersymmetric models are also fine tuned (although to a much lesser extent). We review the traditional measure of this fine tuning used in the literature and propose an alternative. We apply this to the MSSM and show the implications.Comment: Included in proceedings of The 14th International Conference on Supersymmetry and the Unification of Fundamental Interaction

Measuring Fine Tuning In Supersymmetry

The solution to fine tuning is one of the principal motivations for supersymmetry. However constraints on the parameter space of the Minimal Supersymmetric Standard Model (MSSM) suggest it may also require fine tuning (although to a much lesser extent). To compare this tuning with different extensions of the Standard Model (including other supersymmetric models) it is essential that we have a reliable, quantitative measure of tuning. We review the measures of tuning used in the literature and propose an alternative measure. We apply this measure to several toy models and the MSSM with some intriguing results.Comment: Submitted for the SUSY07 proceeding

Asymmetric velocity correlations in shearing media

A model of soft frictionless disks in two dimensions at zero temperature is simulated with a shearing dynamics to study various kinds of asymmetries in sheared systems. We examine both single particle properties, the spatial velocity correlation function, and a correlation function designed to separate clockwise and counter-clockwise rotational fields from one another. Among the rich and interesting behaviors we find that the velocity correlation along the two different diagonals corresponding to compression and dilation, respectively, are almost identical and, furthermore, that a feature in one of the correlation functions is directly related to irreversible plastic events

Field dependent mass enhancement in Pr_{1-x}La_xOs_4Sb_12 from aspherical Coulomb scattering

The scattering of conduction electrons by crystalline electric field (CEF) excitations may enhance their effective quasiparticle mass similar to scattering from phonons. A wellknown example is Pr metal where the isotropic exchange scattering from inelastic singlet-singlet excitations causes the mass enhancement. An analogous mechanism may be at work in the skutterudite compounds Pr_{1-x}La_xOs_4Sb_12 where close to x=1 the compound develops heavy quasiparticles with a large linear specific heat coefficient. There the low lying CEF states are singlet ground state and a triplet at 8 K. Due to the tetrahedral CEF the main scattering mechanism must be the aspherical Coulomb scattering. We derive the expression for mass enhancement in this model including also the case of dispersive excitations. We show that for small to moderate dispersion there is a strongly field dependent mass enhancement due to the field induced triplet splitting. It is suggested that this effect may be seen in Pr_{1-x}La_xOs_4Sb_12 with suitably large x when the dispersion is small.Comment: 12 pages, 5 figure

Calculation of Hydrogenic Bethe Logarithms for Rydberg States

We describe the calculation of hydrogenic (one-loop) Bethe logarithms for all states with principal quantum numbers n <= 200. While, in principle, the calculation of the Bethe logarithm is a rather easy computational problem involving only the nonrelativistic (Schroedinger) theory of the hydrogen atom, certain calculational difficulties affect highly excited states, and in particular states for which the principal quantum number is much larger than the orbital angular momentum quantum number. Two evaluation methods are contrasted. One of these is based on the calculation of the principal value of a specific integral over a virtual photon energy. The other method relies directly on the spectral representation of the Schroedinger-Coulomb propagator. Selected numerical results are presented. The full set of values is available at quant-ph/0504002.Comment: 10 pages, RevTe