Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach

We determine the asymptotic level spacing distribution for the Laguerre Ensemble in a single scaled interval, $(0,s)$, containing no levels, E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the $\alpha=0$ Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by both Edelman and Forrester, while for $\alpha\neq 0$, the leading terms of $E_{2}(0,s)$, found by Tracy and Widom, are reproduced without the use of the Bessel kernel and the associated Painlev\'e transcendent. In the same approximation, the next leading term, due to a ``finite temperature'' perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe

Dirac monopole with Feynman brackets

We introduce the magnetic angular momentum as a consequence of the structure of the sO(3) Lie algebra defined by the Feynman brackets. The Poincare momentum and Dirac magnetic monopole appears as a direct result of this framework.Comment: 10 page

Phonon emission and arrival times of electrons from a single-electron source

In recent charge-pump experiments, single electrons are injected into quantum Hall edge channels at energies significantly above the Fermi level. We consider here the relaxation of these hot edge-channel electrons through longitudinal-optical-phonon emission. Our results show that the probability for an electron in the outermost edge channel to emit one or more phonons en route to a detector some microns distant along the edge channel suffers a double-exponential suppression with increasing magnetic field. This explains recent experimental observations. We also describe how the shape of the arrival-time distribution of electrons at the detector reflects the velocities of the electronic states post phonon emission. We show how this can give rise to pronounced oscillations in the arrival-time-distribution width as a function of magnetic field or electron energy

Relativistic Dyson Rings and Their Black Hole Limit

In this Letter we investigate uniformly rotating, homogeneous and axisymmetric relativistic fluid bodies with a toroidal shape. The corresponding field equations are solved by means of a multi-domain spectral method, which yields highly accurate numerical solutions. For a prescribed, sufficiently large ratio of inner to outer coordinate radius, the toroids exhibit a continuous transition to the extreme Kerr black hole. Otherwise, the most relativistic configuration rotates at the mass-shedding limit. For a given mass-density, there seems to be no bound to the gravitational mass as one approaches the black-hole limit and a radius ratio of unity.Comment: 13 pages, 1 table, 5 figures, v2: some discussion and two references added, accepted for publication in Astrophys. J. Let

Low-Temperature Properties of Two-Dimensional Ideal Ferromagnets

The manifestation of the spin-wave interaction in the low-temperature series of the partition function has been investigated extensively over more than seven decades in the case of the three-dimensional ferromagnet. Surprisingly, the same problem regarding ferromagnets in two spatial dimensions, to the best of our knowledge, has never been addressed in a systematic way so far. In the present paper the low-temperature properties of two-dimensional ideal ferromagnets are analyzed within the model-independent method of effective Lagrangians. The low-temperature expansion of the partition function is evaluated up to two-loop order and the general structure of this series is discussed, including the effect of a weak external magnetic field. Our results apply to two-dimensional ideal ferromagnets which exhibit a spontaneously broken spin rotation symmetry O(3) $\to$ O(2) and are defined on a square, honeycomb, triangular or Kagom\'e lattice. Remarkably, the spin-wave interaction only sets in at three-loop order. In particular, there is no interaction term of order $T^3$ in the low-temperature series for the free energy density. This is the analog of the statement that, in the case of three-dimensional ferromagnets, there is no interaction term of order $T^4$ in the free energy density. We also provide a careful discussion of the implications of the Mermin-Wagner theorem in the present context and thereby put our low-temperature expansions on safe grounds.Comment: 24 pages, 3 figure

Integration over matrix spaces with unique invariant measures

We present a method to calculate integrals over monomials of matrix elements with invariant measures in terms of Wick contractions. The method gives exact results for monomials of low order. For higher--order monomials, it leads to an error of order 1/N^alpha where N is the dimension of the matrix and where alpha is independent of the degree of the monomial. We give a lower bound on the integer alpha and show how alpha can be increased systematically. The method is particularly suited for symbolic computer calculation. Explicit results are given for O(N), U(N) and for the circular orthogonal ensemble.Comment: 12 pages in revtex, no figure

Metalanguage in L1 English-speaking 12-year-olds: which aspects of writing do they talk about?

Traditional psycholinguistic approaches to metalinguistic awareness in L1 learners elicit responses containing metalanguage that demonstrates metalinguistic awareness of pre-determined aspects of language knowledge. This paper, which takes a more ethnographic approach, demonstrates how pupils are able to engage their own focus of metalanguage when reflecting on their everyday learning activities involving written language. What is equally significant is what their metalanguage choices reveal about their understanding and application of written language concepts

Anderson transitions in three-dimensional disordered systems with randomly varying magnetic flux

The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer matrix method with high accuracy. Both, systems with and without an additional random scalar potential are considered. We find a critical exponent of $\nu=1.45\pm0.09$ with random scalar potential. Without it, $\nu$ is smaller but increases with the system size and extrapolates within the error bars to a value close to the above. The present results support the conventional classification of universality classes due to symmetry.Comment: 4 pages, 2 figures, to appear in Phys. Rev.

Energy level statistics for models of coupled single-mode Bose--Einstein condensates

We study the distribution of energy level spacings in two models describing coupled single-mode Bose-Einstein condensates. Both models have a fixed number of degrees of freedom, which is small compared to the number of interaction parameters, and is independent of the dimensionality of the Hilbert space. We find that the distribution follows a universal Poisson form independent of the choice of coupling parameters, which is indicative of the integrability of both models. These results complement those for integrable lattice models where the number of degrees of freedom increases with increasing dimensionality of the Hilbert space. Finally, we also show that for one model the inclusion of an additional interaction which breaks the integrability leads to a non-Poisson distribution.Comment: 5 pages, 4 figures, revte

Functional dynamics of the folded ankyrin repeats of I kappa B alpha revealed by nuclear magnetic resonance.

Inhibition of nuclear factor kappaB (NF-kappaB) is mainly accomplished by IkappaB alpha, which consists of a signal response sequence at the N-terminus, a six-ankyrin repeat domain (ARD) that binds NF-kappaB, and a C-terminal PEST sequence. Previous studies with the ARD revealed that the fifth and sixth repeats are only partially folded in the absence of NF-kappaB. Here we report NMR studies of a truncated version of IkappaB alpha, containing only the first four ankyrin repeats, IkappaB alpha(67-206). This four-repeat segment is well-structured in the free state, enabling full resonance assignments to be made. H-D exchange, backbone dynamics, and residual dipolar coupling (RDC) experiments reveal regions of flexibility. In addition, regions consistent with the presence of micro- to millisecond motions occur periodically throughout the repeat structure. Comparison of the RDCs with the crystal structure gave only moderate agreement, but an ensemble of structures generated by accelerated molecular dynamics gave much better agreement with the measured RDCs. The regions showing flexibility correspond to those implicated in entropic compensation for the loss of flexibility in ankyrin repeats 5 and 6 upon binding to NF-kappaB. The regions showing micro- to millisecond motions in the free protein are the ends of the beta-hairpins that directly interact with NF-kappaB in the complex