Haldane fractional statistics in the fractional quantum Hall effect

We have tested Haldane's ``fractional-Pauli-principle'' description of excitations around the $\nu = 1/3$ state in the FQHE, using exact results for small systems of electrons. We find that Haldane's prediction $\beta = \pm 1/m$ for quasiholes and quasiparticles, respectively, describes our results well with the modification $\beta_{qp} = 2-1/3$ rather than $-1/3$. We also find that this approach enables us to better understand the {\it energetics\/} of the ``daughter'' states; in particular, we find good evidence, in terms of the effective interaction between quasiparticles, that the states $\nu = 4/11$ and 4/13 should not be stable.Comment: 9 pages, 3 Postscript figures, RevTex 3.0. (UCF-CM-93-005

Estimating the Spatial Extent of Attractors of Iterated Function System

Technical Report for Period January 1993 - April 1993From any given Iterated Function System, a small set of balls that cover the fractal attractor can be simply determined. This gives a priori bounds on the region of space in which the attractor may be constructed.Naval Postgraduate SchoolApproved for public release; distribution is unlimited

Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part I: epsilon-Machine Spectral Reconstruction Theory

In a recent publication [D. P. Varn, G. S. Canright, and J. P. Crutchfield, Phys. Rev. B {\bf 66}:17, 156 (2002)] we introduced a new technique for discovering and describing planar disorder in close-packed structures (CPSs) directly from their diffraction spectra. Here we provide the theoretical development behind those results, adapting computational mechanics to describe one-dimensional structure in materials. By way of contrast, we give a detailed analysis of the current alternative approach, the fault model (FM), and offer several criticisms. We then demonstrate that the computational mechanics description of the stacking sequence--in the form of an epsilon-machine--provides the minimal and unique description of the crystal, whether ordered, disordered, or some combination. We find that we can detect and describe any amount of disorder, as well as materials that are mixtures of various kinds of crystalline structure. Underlying this approach is a novel method for epsilon-machine reconstruction that uses correlation functions estimated from diffraction spectra, rather than sequences of microscopic configurations, as is typically used in other domains. The result is that the methods developed here can be adapted to a wide range of experimental systems in which spectroscopic data is available.Comment: 26 pages, 23 figures, 8 tables, 110 citations; http://www.santafe.edu/projects/CompMech/papers/ipdcpsi.htm

Inferring Pattern and Disorder in Close-Packed Structures from X-ray Diffraction Studies, Part II: Structure and Intrinsic Computation in Zinc Sulphide

In the previous paper of this series [D. P. Varn, G. S. Canright, and J. P. Crutchfield, Physical Review B, submitted] we detailed a procedure--epsilon-machine spectral reconstruction--to discover and analyze patterns and disorder in close-packed structures as revealed in x-ray diffraction spectra. We argued that this computational mechanics approach is more general than the current alternative theory, the fault model, and that it provides a unique characterization of the disorder present. We demonstrated the efficacy of computational mechanics on four prototype spectra, finding that it was able to recover a statistical description of the underlying modular-layer stacking using epsilon-machine representations. Here we use this procedure to analyze structure and disorder in four previously published zinc sulphide diffraction spectra. We selected zinc sulphide not only for the theoretical interest this material has attracted in an effort to develop an understanding of polytypism, but also because it displays solid-state phase transitions and experimental data is available.Comment: 15 pages, 14 figures, 4 tables, 57 citations; http://www.santafe.edu/projects/CompMech/papers/ipdcpsii.htm

Analytical solution for the Fermi-sea energy of two-dimensional electrons in a magnetic field: lattice path-integral approach and quantum interference

We derive an exact solution for the total kinetic energy of noninteracting spinless electrons at half-filling in two-dimensional bipartite lattices. We employ a conceptually novel approach that maps this problem exactly into a Feynman-Vdovichenko lattice walker. The problem is then reduced to the analytic study of the sum of magnetic phase factors on closed paths. We compare our results with the ones obtained through numerical calculations.Comment: 5 pages, RevTe

Acoustic interactions in arrays of spherical elastic shells

The article of record as published may be located at http://dx.doi.org/10.1121/1.401233The acoustical performance of a submerged linear array of spherical transducers is examined by combining the T-Matrix method of solving for multiple acoustic interactions among separate bodies with a model for the transducers as thin spherical elastic shells. This approach solves the fully coupled problem of the response of the array to internal forcing. The results show that the assumptions giving rise to the Chebyshev criteria for optimal arrays of point sources appear to apply well even for large spheres at low frequencies. However, at frequencies near or above the lowest resonant frequency the directional pattern may be degraded, depending on the material of the shells

The effects of heat treatments on ectomycorrhizal resistant propagules and their ability to colonize bioassay seedlings

The effect of disturbance on the resistant propagule community (RPC) of ectomycorrhizal fungi has been given relatively little attention. In this study we investigate the effects of heat, one important factor of fire disturbances, on the ability of ectomycorrhizal RPC fungi to colonize Pinus jeffreyi seedlings in greenhouse bioassays. Prior to planting the seed, soils were collected from an old growth mixed-conifer forest in the southern Sierra Nevada, California, USA and then subjected to four heat treatments of none, 45 C, 60 C, and 75 C. After eight months, seedlings were harvested and the ectomycorrhizal fungi colonizing the roots were characterized by molecular methods (PCR-RFLP and DNA sequencing). Rhizopogon species increased in dominance on seedlings grown in soils receiving the 75 C heat treatment. One species significantly increased in frequency, Rhizopogon olivaceotinctus, and two species (Cenococcum geophilum and Wilcoxina sp.) significantly decreased in frequency in the 75 C treatment. The increase of R. olivaceotinctus, coupled with other features of its behavior, suggests that substantial heat disturbances may benefit this species in competing for roots.Keywords: Rhizopogon, Phoenicoid fungi, Ruderal species, Basidiospores, Heat disturbanc

Exclusion statistics for fractional quantum Hall states on a sphere

We discuss exclusion statistics parameters for quasiholes and quasielectrons excited above the fractional quantum Hall states near $\nu=p/(2np+1)$. We derive the diagonal statistics parameters from the (``unprojected'') composite fermion (CF) picture. We propose values for the off-diagonal (mutual) statistics parameters as a simple modification of those obtained from the unprojected CF picture, by analyzing finite system numerical spectra in the spherical geometry.Comment: 9 pages, Revtex, 4 Postscript figures. Universality of the statistics parameters is stressed, 2 figs adde