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

Systematic Renormalization in Hamiltonian Light-Front Field Theory: The Massive Generalization

Hamiltonian light-front field theory can be used to solve for hadron states in QCD. To this end, a method has been developed for systematic renormalization of Hamiltonian light-front field theories, with the hope of applying the method to QCD. It assumed massless particles, so its immediate application to QCD is limited to gluon states or states where quark masses can be neglected. This paper builds on the previous work by including particle masses non-perturbatively, which is necessary for a full treatment of QCD. We show that several subtle new issues are encountered when including masses non-perturbatively. The method with masses is algebraically and conceptually more difficult; however, we focus on how the methods differ. We demonstrate the method using massive phi^3 theory in 5+1 dimensions, which has important similarities to QCD.Comment: 7 pages, 2 figures. Corrected error in Eq. (11), v3: Added extra disclaimer after Eq. (2), and some clarification at end of Sec. 3.3. Final published versio

Distribution of the Riemann zeros represented by the Fermi gas

The multiparticle density matrices for degenerate, ideal Fermi gas system in any dimension are calculated. The results are expressed as a determinant form, in which a correlation kernel plays a vital role. Interestingly, the correlation structure of one-dimensional Fermi gas system is essentially equivalent to that observed for the eigenvalue distribution of random unitary matrices, and thus to that conjectured for the distribution of the non-trivial zeros of the Riemann zeta function. Implications of the present findings are discussed briefly.Comment: 7 page

Eigenvalue correlations on Hyperelliptic Riemann surfaces

In this note we compute the functional derivative of the induced charge density, on a thin conductor, consisting of the union of g+1 disjoint intervals, $J:=\cup_{j=1}^{g+1}(a_j,b_j),$ with respect to an external potential. In the context of random matrix theory this object gives the eigenvalue fluctuations of Hermitian random matrix ensembles where the eigenvalue density is supported on J.Comment: latex 2e, seven pages, one figure. To appear in Journal of Physics

Initial Ionization of Compressible Turbulence

We study the effects of the initial conditions of turbulent molecular clouds on the ionization structure in newly formed H_{ii} regions, using three-dimensional, photon-conserving radiative transfer in a pre-computed density field from three-dimensional compressible turbulence. Our results show that the initial density structure of the gas cloud can play an important role in the resulting structure of the H_{ii} region. The propagation of the ionization fronts, the shape of the resulting H_{ii} region, and the total mass ionized depend on the properties of the turbulent density field. Cuts through the ionized regions generally show ``butterfly'' shapes rather than spherical ones, while emission measure maps are more spherical if the turbulence is driven on scales small compared to the size of the H_{ii} region. The ionization structure can be described by an effective clumping factor $\zeta=< n > \cdot /^2$, where $n$ is number density of the gas. The larger the value of $\zeta$, the less mass is ionized, and the more irregular the H_{ii} region shapes. Because we do not follow dynamics, our results apply only to the early stage of ionization when the speed of the ionization fronts remains much larger than the sound speed of the ionized gas, or Alfv\'en speed in magnetized clouds if it is larger, so that the dynamical effects can be negligible.Comment: 9 pages, 10 figures, version with high quality color images can be found in http://research.amnh.org/~yuexing/astro-ph/0407249.pd

Quantum Heisenberg Chain with Long-Range Ferromagnetic Interactions at Low Temperature

A modified spin-wave theory is applied to the one-dimensional quantum Heisenberg model with long-range ferromagnetic interactions. Low-temperature properties of this model are investigated. The susceptibility and the specific heat are calculated; the relation between their behaviors and strength of the long-range interactions is obtained. This model includes both the Haldane-Shastry model and the nearest-neighbor Heisenberg model; the corresponding results in this paper are in agreement with the solutions of both the models. It is shown that there exists an ordering transition in the region where the model has longer-range interactions than the HS model. The critical temperature is estimated.Comment: 17 pages(LaTeX REVTeX), 1 figure appended (PostScript), Technical Report of ISSP A-274

Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons

We calculate the exact dynamical magnetic structure factor S(Q,E) in the ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2 spinon excitations, the Haldane-Shastry model with inverse-square exchange, which is in the same low-energy universality class as Bethe's nearest-neighbor exchange model. Only two-spinon excited states contribute, and S(Q,E) is found to be a very simple integral over these states.Comment: 11 pages, LaTeX, RevTeX 3.0, cond-mat/930903

Magnetic properties of quantum Heisenberg ferromagnets with long-range interactions

Quantum Heisenberg ferromagnets with long-range interactions decayin as $1/r^p$ in one and two dimensions are investigated by means of the Green's function method. It is shown that there exists a finite-temperature phase transition in the region $d<p<2 d$ for the $d$-dimensional case and that no transitions at any finite temperature exist for $p\ge 2 d$; the critical temperature is also estimated. We study the magnetic properties of this model. We calculate the critical exponents' dependence on $p$; these exponents also satisfy a scaling relation. Some of the results were also found using the modified spin-wave theory and are in remarkable agreement with each other.Comment: 13 pages(LaTeX REVTeX), 2 figures not included (postscript files available on request), submitted to 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

Introduction to Random Matrices

These notes provide an introduction to the theory of random matrices. The central quantity studied is $\tau(a)= det(1-K)$ where $K$ is the integral operator with kernel 1/\pi} {\sin\pi(x-y)\over x-y} \chi_I(y). Here $I=\bigcup_j(a_{2j-1},a_{2j})$ and $\chi_I(y)$ is the characteristic function of the set $I$. In the Gaussian Unitary Ensemble (GUE) the probability that no eigenvalues lie in $I$ is equal to $\tau(a)$. Also $\tau(a)$ is a tau-function and we present a new simplified derivation of the system of nonlinear completely integrable equations (the $a_j$'s are the independent variables) that were first derived by Jimbo, Miwa, M{\^o}ri, and Sato in 1980. In the case of a single interval these equations are reducible to a Painlev{\'e} V equation. For large $s$ we give an asymptotic formula for $E_2(n;s)$, which is the probability in the GUE that exactly $n$ eigenvalues lie in an interval of length $s$.Comment: 44 page