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Fractional Quantum Hall Hierarchy and the Second Landau Level
Get PDFWe generalize the Haldane-Halperin hierarchy picture to apply to arbitrary, possibly non-Abelian, fractional quantum Hall states. Using this, we propose trial wave functions to describe the observed Hall conductance plateaus in the second Landau level. These hierarchy states are constructed over the Moore-Read state, the expected description of the ν = 5/2 plateau, such that the quasiparticle gases generating the hierarchization only involve excitations from the electric charge sector. These proposed states all have electron pairing in the ground state and an excitation spectrum that includes non-Abelian anyons of the Ising model σ-vortex type
On Some Lie Bialgebra Structures on Polynomial Algebras and their Quantization
Get PDFWe study classical twists of Lie bialgebra structures on the polynomial current algebra g[u], where g is a simple complex finite-dimensional Lie algebra. We focus on the structures induced by the so-called quasi-trigonometric solutions of the classical Yang-Baxter equation. It turns out that quasi-trigonometric r-matrices fall into classes labelled by the vertices of the extended Dynkin diagram of g. We give complete classification of quasi-trigonometric r-matrices belonging to multiplicity free simple roots (which have coefficient 1 in the decomposition of the maximal root). We quantize solutions corresponding to the first root of sl(n)
Fuzzy scalar field theory as a multitrace matrix model
Get PDFWe develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular degrees of freedom in the hermitian matrices encoding the scalar field. The remaining model depends only on the eigenvalues of the matrices and corresponds to a multitrace hermitian matrix model. Such a model can be solved by standard techniques as e.g. the saddle-point approximation. We evaluate the perturbative expansion up to second order and present the one-cut solution of the saddle-point approximation in the large N limit. We apply our approach to a model which has been proposed as an appropriate regularization of scalar field theory on the plane within the framework of fuzzy geometry
Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
Get PDFQuantum models on the hyper-cubic d-dimensional lattice of spin-1/2 particles inter-acting with linear oscillators are shown to have three ferromagnetic ground state order parameters. Two order parameters coincide with the magnetization in the first and third directions and the third one is a magnetization in a continuous oscillator variable. The proofs use a generalized Peierls argument and two Griffiths inequalities. The class of spin-oscillator Hamiltonians considered manifest maximal ordering in their ground states. The models have relevance for hydrogen-bond ferroelectrics. The simplest of these is proven to have a unique Gibbsian ground state
A Multitrace Matrix Model from Fuzzy Scalar Field Theory
Get PDFWe present the analytical approach to scalar field theory on the fuzzy sphere which has been developed in hep-th/0706.2493. This approach is based on considering a perturbative expansion of the kinetic term in the partition function. After truncating this expansion at second order, one arrives at a multitrace matrix model, which allows for an application of the saddle-point method. The results are in agreement with the numerical findings in the literature
The Irish of Iorras Aithneach, County Galway; Volume I
Get PDFThis grammar is based on extensive fieldwork, published and unpublished lore, and recent as well as older recordings, particularly those held in the archives of Roinn Bhéaloideas Éireann and Raidió na Gaeltachta. These sources provide a picture of extensive variation and change across the six generations born between 1850 and 2000. The grammar draws on several branches of linguistics: descriptive and historical linguistics, dialectology and sociolinguistics. It is the most comprehensive treatment of any variety of Irish.
Volume I provides an introduction and chapters on historical phonology, sandhi and nominal morphology
Einstein-Yang-Mills solutions in higher dimensional de Sitter spacetime
Get PDFWe consider particle-like and black holes solutions of the Einstein-Yang-Mills system with positive cosmological constant in d > 4 spacetime dimensions. These configurations are spherically symmetric and present a cosmological horizon for a finite value of the radial coordinate, approaching asymptotically the de Sitter background. In the usual Yang–Mills case we find that the mass of these solutions, evaluated outside the cosmological horizon at future/past infinity generically diverges for d > 4. Solutions with finite mass are found by adding to the action higher order gauge field terms belonging to the Yang–Mills hierarchy. A discussion of the main properties of these solutions and their differences from those to the usual Yang–Mills model, both in four and higher dimensions is presented
