Kinetic theory for strong uniform shear flow of granular media at high density

We discuss the uniform shear flow of a fluidized granular bed composed of monodisperse Hertzian spheres. Considering high densities around the glass transition density of inelastic Hertzian spheres, we report kinetic theory expressions for the Newtonian viscosity as well as the Bagnold coefficient. We discuss the dependence of the transport coefficients on density and coefficient of restitution.Comment: Powders & Grains 201

Charge correlations in the weakly doped t-J model calculated by projection technique

We study frequency- and wave-vector dependent charge correlations in weakly doped antiferromagnets using Mori-Zwanzig projection technique. The system is described by the two-dimensional t-J model. The ground state is expressed within a cumulant formalism which has been successfully applied to study magnetic properties of the weakly doped system. Within this approach the ground state contains independent spin-bag quasiparticles (magnetic polarons). We present results for the charge-density response function and for the optical conductivity at zero temperature for different values of t/J. They agree well with numerical results calculated by exact diagonalization techniques. The density response function for intermediate and large momenta shows a broad continuum on energy scales of order of several t whereas the optical conductivity for \omega > 0 is dominated by low energy excitations (at 1.5 - 2 J). We show that these weak-doping properties can be well understood by transitions between excited states of spin-bag quasiparticles.Comment: 10 pages, 5 figs., to appear in Europ. Phys. J.

Asymptotics of Clebsch-Gordan Coefficients

Asymptotic expressions for Clebsch-Gordan coefficients are derived from an exact integral representation. Both the classically allowed and forbidden regions are analyzed. Higher-order approximations are calculated. These give, for example, six digit accuracy when the quantum numbers are in the hundreds.Comment: 30 pages, two figures. New Appendix added. Accepted for publication in the Journal of Mathematical Physic

A short introduction to Fibonacci anyon models

We discuss how to construct models of interacting anyons by generalizing quantum spin Hamiltonians to anyonic degrees of freedom. The simplest interactions energetically favor pairs of anyons to fuse into the trivial ("identity") channel, similar to the quantum Heisenberg model favoring pairs of spins to form spin singlets. We present an introduction to the theory of anyons and discuss in detail how basis sets and matrix representations of the interaction terms can be obtained, using non-Abelian Fibonacci anyons as example. Besides discussing the "golden chain", a one-dimensional system of anyons with nearest neighbor interactions, we also present the derivation of more complicated interaction terms, such as three-anyon interactions in the spirit of the Majumdar-Ghosh spin chain, longer range interactions and two-leg ladders. We also discuss generalizations to anyons with general non-Abelian su(2)_k statistics. The k to infinity limit of the latter yields ordinary SU(2) spin chains

Calculation and spectroscopy of the Landau band structure at a thin and atomically precise tunneling barrier

Two laterally adjacent quantum Hall systems separated by an extended barrier of a thickness on the order of the magnetic length possess a complex Landau band structure in the vicinity of the line junction. The energy dispersion is obtained from an exact quantum-mechanical calculation of the single electron eigenstates for the coupled system by representing the wave functions as a superposition of parabolic cylinder functions. For orbit centers approaching the barrier, the separation of two subsequent Landau levels is reduced from the cyclotron energy to gaps which are much smaller. The position of the anticrossings increases on the scale of the cyclotron energy as the magnetic field is raised. In order to experimentally investigate a particular gap at different field strengths but under constant filling factor, a GaAs/AlGaAs heterostructure with a 52 Angstrom thick tunneling barrier and a gate electrode for inducing the two-dimensional electron systems was fabricated by the cleaved edge overgrowth method. The shift of the gaps is observed as a displacement of the conductance peaks on the scale of the filling factor. Besides this effect, which is explained within the picture of Landau level mixing for an ideal barrier, we report on signatures of quantum interferences at imperfections of the barrier which act as tunneling centers. The main features of the recent experiment of Yang, Kang et al. are reproduced and discussed for different gate voltages. Quasiperiodic oscillations, similar to the Aharonov Bohm effect at the quenched peak, are revealed for low magnetic fields before the onset of the regular conductance peaks.Comment: 8 pages, 10 figures, 1 tabl

Magnetic properties and spin waves of bilayer magnets in a uniform field

The two-layer square lattice quantum antiferromagnet with spins 1/2 shows a zero-field magnetic order-disorder transition at a critical ratio of the inter-plane to intra-plane couplings. Adding a uniform magnetic field tunes the system to canted antiferromagnetism and eventually to a fully polarized state; similar behavior occurs for ferromagnetic intra-plane coupling. Based on a bond operator spin representation, we propose an approximate ground state wavefunction which covers all phases by means of a unitary transformation. The excitations can be efficiently described as independent bosons; in the antiferromagnetic phase these reduce to the well-known spin waves, whereas they describe gapped spin-1 excitations in the singlet phase. We compute the spectra of these excitations as well as the magnetizations throughout the whole phase diagram.Comment: 12 pages, 9 figs; added references; final version as publishe