A new Proposal for a Quasielectron Trial Wavefunction for the FQHE on a Disk

In this letter, we propose a new quasielectron trial wavefunction for $N$ interacting electrons in two dimensions moving in a strong magnetic field in a disk geometry. Requiring that the trial wavefunction exhibits the correct filling factor of a quasielectron wavefunction, we obtain $N+1$ angular momentum eigenfunctions. The expectation values of the energy are calculated and compared with the data of an exact numerical diagonalization.Comment: 8 page

Extrinsic Curvature Embedding Diagrams

Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an extrinsic curvature embedding diagram, when used together with the usual kind of intrinsic curvature embedding diagram, carries the information of how a surface is {\it embedded} in the higher dimensional curved space. Simple examples are given to illustrate the idea.Comment: 22 pages, 4 figure

Global embedding of D-dimensional black holes with a cosmological constant in Minkowskian spacetimes: Matching between Hawking temperature and Unruh temperature

We study the matching between the Hawking temperature of a large class of static D-dimensional black holes and the Unruh temperature of the corresponding higher dimensional Rindler spacetime. In order to accomplish this task we find the global embedding of the D-dimensional black holes into a higher dimensional Minkowskian spacetime, called the global embedding Minkowskian spacetime procedure (GEMS procedure). These global embedding transformations are important on their own, since they provide a powerful tool that simplifies the study of black hole physics by working instead, but equivalently, in an accelerated Rindler frame in a flat background geometry. We discuss neutral and charged Tangherlini black holes with and without cosmological constant, and in the negative cosmological constant case, we consider the three allowed topologies for the horizons (spherical, cylindrical/toroidal and hyperbolic).Comment: 7 pages; ReVTeX

Berry phases for composite fermions: effective magnetic field and fractional statistics

The quantum Hall superfluid is presently the only viable candidate for a realization of quasiparticles with fractional Berry phase statistics. For a simple vortex excitation, relevant for a subset of fractional Hall states considered by Laughlin, non-trivial Berry phase statistics were demonstrated many years ago by Arovas, Schrieffer, and Wilczek. The quasiparticles are in general more complicated, described accurately in terms of excited composite fermions. We use the method developed by Kjonsberg, Myrheim and Leinaas to compute the Berry phase for a single composite-fermion quasiparticle, and find that it agrees with the effective magnetic field concept for composite fermions. We then evaluate the "fractional statistics", related to the change in the Berry phase for a closed loop caused by the insertion of another composite-fermion quasiparticle in the interior. Our results support the general validity of fractional statistics in the quantum Hall superfluid, while also giving a quantitative account of corrections to it when the quasiparticle wave functions overlap. Many caveats, both practical and conceptual, are mentioned that will be relevant to an experimental measurement of the fractional statistics. A short report on some parts of this article has appeared previously.Comment: 14 pages, 9 figure

Analytic Coulomb matrix elements in the lowest Landau level in disk geometry

Using Darling's theorem on products of generalized hypergeometric series an analytic expression is obtained for the Coulomb matrix elements in the lowest Landau level in the representation of angular momentum. The result is important in the studies of Fractional Quantum Hall effect (FQHE) in disk geometry. Matrix elements are expressed as simple finite sums of positive terms, eliminating the need to approximate these quantities with slowly-convergent series. As a by-product, an analytic representation for certain integals of products of Laguerre polynomials is obtained.Comment: Accepted to J. Math. Phys.; 3 pages revtex, no figure

Expanding Cosmologies in Brane Geometries

Five dimensional gravity coupled, both in the bulk and on a brane, to a scalar Liouville field yields a geometry confined to a strip around the brane and with time dependent scale factors for the four geometry. In various limits known models can be recovered as well as a temporally expanding four geometry with a warp factor falling exponentially away from the brane. The effective theory on the brane has a time dependent Planck mass and ``cosmological constant''. Although the scale factor expands, the expansion is not an acceleration.Comment: 7 pages, LaTex/RevTex

A maximum density rule for surfaces of quasicrystals

A rule due to Bravais of wide validity for crystals is that their surfaces correspond to the densest planes of atoms in the bulk of the material. Comparing a theoretical model of i-AlPdMn with experimental results, we find that this correspondence breaks down and that surfaces parallel to the densest planes in the bulk are not the most stable, i.e. they are not so-called bulk terminations. The correspondence can be restored by recognizing that there is a contribution to the surface not just from one geometrical plane but from a layer of stacked atoms, possibly containing more than one plane. We find that not only does the stability of high-symmetry surfaces match the density of the corresponding layer-like bulk terminations but the exact spacings between surface terraces and their degree of pittedness may be determined by a simple analysis of the density of layers predicted by the bulk geometric model.Comment: 8 pages of ps-file, 3 Figs (jpg