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

Fluctuation properties of strength functions associated with giant resonances

We performed fluctuation analysis by means of the local scaling dimension for the strength function of the isoscalar (IS) and the isovector (IV) giant quadrupole resonances (GQR) in $^{40}$Ca, where the strength functions are obtained by the shell model calculation within up to the 2p2h configurations. It is found that at small energy scale, fluctuation of the strength function almost obeys the Gaussian orthogonal ensemble (GOE) random matrix theory limit. On the other hand, we found a deviation from the GOE limit at the intermediate energy scale about 1.7MeV for the IS and at 0.9MeV for the IV. The results imply that different types of fluctuations coexist at different energy scales. Detailed analysis strongly suggests that GOE fluctuation at small energy scale is due to the complicated nature of 2p2h states and that fluctuation at the intermediate energy scale is associated with the spreading width of the Tamm-Dancoff 1p1h states.Comment: 14 pages including 13figure

Wigner-Dyson Statistics from the Replica Method

We compute the correlation functions of the eigenvalues in the Gaussian unitary ensemble using the fermionic replica method. We show that non--trivial saddle points, which break replica symmetry, must be included in the calculation in order to reproduce correctly the exact results for the correlation functions at large distance.Comment: 13 pages, added reference

Impact of localization on Dyson's circular ensemble

A wide variety of complex physical systems described by unitary matrices have been shown numerically to satisfy level statistics predicted by Dyson's circular ensemble. We argue that the impact of localization in such systems is to provide certain restrictions on the eigenvalues. We consider a solvable model which takes into account such restrictions qualitatively and find that within the model a gap is created in the spectrum, and there is a transition from the universal Wigner distribution towards a Poisson distribution with increasing localization.Comment: To be published in J. Phys.

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

Instabilities in complex mixtures with a large number of components

Inside living cells are complex mixtures of thousands of components. It is hopeless to try to characterise all the individual interactions in these mixtures. Thus, we develop a statistical approach to approximating them, and examine the conditions under which the mixtures phase separate. The approach approximates the matrix of second virial coefficients of the mixture by a random matrix, and determines the stability of the mixture from the spectrum of such random matrices.Comment: 4 pages, uses RevTeX 4.

Statistical Analysis of Magnetic Field Spectra

We have calculated and statistically analyzed the magnetic-field spectrum (the ``B-spectrum'') at fixed electron Fermi energy for two quantum dot systems with classically chaotic shape. This is a new problem which arises naturally in transport measurements where the incoming electron has a fixed energy while one tunes the magnetic field to obtain resonance conductance patterns. The ``B-spectrum'', defined as the collection of values ${B_i}$ at which conductance $g(B_i)$ takes extremal values, is determined by a quadratic eigenvalue equation, in distinct difference to the usual linear eigenvalue problem satisfied by the energy levels. We found that the lower part of the ``B-spectrum'' satisfies the distribution belonging to Gaussian Unitary Ensemble, while the higher part obeys a Poisson-like behavior. We also found that the ``B-spectrum'' fluctuations of the chaotic system are consistent with the results we obtained from random matrices

Long-Lived Venus Lander Conceptual Design: How To Keep It Cool

Surprisingly little is known about Venus, our neighboring sister planet in the solar system, due to the challenges of operating in its extremely hot, corrosive, and dense environment. For example, after over two dozen missions to the planet, the longest-lived lander was the Soviet Venera 13, and it only survived two hours on the surface. Several conceptual Venus mission studies have been formulated in the past two decades proposing lander architectures that potentially extend lander lifetime. Most recently, the Venus Science and Technology Definition Team (STDT) was commissioned by NASA to study a Venus Flagship Mission potentially launching in the 2020- 2025 time-frame; the reference lander of this study is designed to survive for only a few hours more than Venera 13 launched back in 1981! Since Cytherean mission planners lack a viable approach to a long-lived surface architecture, specific scientific objectives outlined in the National Science Foundation Decadal Survey and Venus Exploration Advisory Group final report cannot be completed. These include: mapping the mineralogy and composition of the surface on a planetary scale determining the age of various rock samples on Venus, searching for evidence of changes in interior dynamics (seismometry) and its impact on climate and many other key observations that benefit with time scales of at least a full Venus day (Le. daylight/night cycle). This report reviews those studies and recommends a hybrid lander architecture that can survive for at least one Venus day (243 Earth days) by incorporating selective Stirling multi-stage active cooling and hybrid thermoacoustic power

Fluctuating Dimension in a Discrete Model for Quantum Gravity Based on the Spectral Principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric and dimension can fluctuate. The model describes the geometry of spaces with a countable number $n$ of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value $$, the average number of points in the universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of$$. Moreover, the space-time dimension $\delta$ is a dynamical observable in our model, and plays the role of an order parameter. The computation of $$ is discussed and an upper bound is found, $< 2$.Comment: 10 pages, no figures. Third version: This new version emphasizes the spectral principle rather than the spectral action. Title has been changed accordingly. We also reformulated the computation of the dimension, and added a new reference. To appear in Physical Review Letter

Rotational Feshbach Resonances in Ultracold Molecular Collisions

In collisions at ultralow temperatures, molecules will possess Feshbach resonances, foreign to ultracold atoms, whose virtual excited states consist of rotations of the molecules. We estimate the mean spacing and mean widths of these resonant states, exploiting the fact the molecular collisions at low energy display chaotic motion. As examples, we consider the experimentally relevant molecules O_2, OH, and PbO. The density of s-wave resonant states for these species is quite high, implying that a large number of narrow resonant states will exist.Comment: 4 pages, 2 figure