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

A Framework for the Landscape

It seems likely that string theory has a landscape of vacua that includes very many metastable de Sitter spaces. However, as emphasized by Banks, Dine and Gorbatov, no current framework exists for examining these metastable vacua in string theory. In this paper we attempt to correct this situation by introducing an eternally inflating background in which the entire collection of accelerating cosmologies is present as intermediate states. The background is a classical solution which consists of a bubble of zero cosmological constant inside de Sitter space, separated by a domain wall. At early and late times the flat space region becomes infinitely big, so an S-matrix can be defined. Quantum mechanically, the system can tunnel to an intermediate state which is pure de Sitter space. We present evidence that a string theory S-matrix makes sense in this background and contains metastable de Sitter space as an intermediate state.Comment: 29+13 pages, 25 figures; v2: minor corrections, references adde

Testing statistical bounds on entanglement using quantum chaos

Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems, investigated recently, entails an universal distribution of the eigenvalues of the reduced density matrices. We demonstrate that these distributions are realized in quantized chaotic systems by using a model of two coupled and kicked tops. We derive an explicit statistical universal bound on entanglement, that is also valid for the case of unequal dimensionality of the Hilbert spaces involved, and show that this describes well the bounds observed using composite quantized chaotic systems such as coupled tops.Comment: 5 pages, 3 figures, to appear in PRL. New title. Revised abstract and some changes in the body of the pape

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

High Resolution CO and H2 Molecular Line Imaging of a Cometary Globule in the Helix Nebula

We report high resolution imaging of a prominent cometary globule in the Helix nebula in the CO J=1-0 (2.6 mm) and H2 v=1-0 S(1) (2.12 micron) lines. The observations confirm that globules consist of dense condensations of molecular gas embedded in the ionized nebula. The head of the globule is seen as a peak in the CO emission with an extremely narrow line width (0.5 km/s) and is outlined by a limb-brightened surface of H2 emission facing the central star and lying within the photo-ionized halo. The emission from both molecular species extends into the tail region. The presence of this extended molecular emission provides new constraints on the structure of the tails, and on the origin and evolution of the globules.Comment: 12 pages, 3 figures. To appear in The Astrophysical Journal Letter

Renormalized Effective QCD Hamiltonian: Gluonic Sector

Extending previous QCD Hamiltonian studies, we present a new renormalization procedure which generates an effective Hamiltonian for the gluon sector. The formulation is in the Coulomb gauge where the QCD Hamiltonian is renormalizable and the Gribov problem can be resolved. We utilize elements of the Glazek and Wilson regularization method but now introduce a continuous cut-off procedure which eliminates non-local counterterms. The effective Hamiltonian is then derived to second order in the strong coupling constant. The resulting renormalized Hamiltonian provides a realistic starting point for approximate many-body calculations of hadronic properties for systems with explicit gluon degrees of freedom.Comment: 25 pages, no figures, revte

Justification of c-Number Substitutions in Bosonic Hamiltonians

The validity of substituting a c-number $z$ for the $k=0$ mode operator $a_0$ is established rigorously in full generality, thereby verifying one aspect of Bogoliubov's 1947 theory. This substitution not only yields the correct value of thermodynamic quantities like the pressure or ground state energy, but also the value of $|z|^2$ that maximizes the partition function equals the true amount of condensation in the presence of a gauge-symmetry breaking term -- a point that had previously been elusive.Comment: RevTeX4, 4pages; minor modifications in the text; final version, to appear in Phys. Rev. Let

RELATIONSHIP OF SHOE IMPACT, BRAKING AND PROPULSIVE FORCE

INTRODUCTION -Van Mechelen (1992) reported that runners having no preference for shoe brand sustained significantly fewer injuries This work aimed to investigate the influence of shoe type on ground reaction force during jogging. Ground reaction forces (vertical, anterior-posterior, mediolateral) were measured as the subjects right foot struck a 9581 Kistler force platform mounted in an outdoor profiex artificial track surface. Forces were sampled and stored using Orthodata Provec software running on a Viglen 386 computer system. Twelve sports students, six male (age 20.17 ±0.75 years; height 180 ±0,07m; weight 81.2 ± 7.0Kg (mean ±S.D)) and six female (age 19.7 ± 0.52 years; height 1.58 ± 0.15m; weight 61.0 ± 8.2Kg (mean ±S,D.)) were the subjects of the study. Following shoe habituation subjects jogged at preferred pace naturally in mild, dry conditions across the platform at least five consecutive times wearing each pair of shoes. Males wore 6 new pairs of shoes (Adidas Response Lite; Adidas Torsion Advance; Tech Performance; Puma Disc system TX4000; Puma Viento; Mizuno Mondo Elite) and females four pairs of shoes (Adidas Response Lite; Adidas Lady Tech Performance; Puma T-400; Puma liberte 11) in an individual random order. Jogging speeds were measured using infrared timing devices positioned 1m before and 1m after the force platform. Peak Forces were read subsequently from the computer screen using cursor measurement to locate peak forces. Following initial evaluation analysis was focused on the vertical and anterior-posterior torees. Mean peak vertical impact and maximal forces, mean peak braking and propulsive forces were expressed relative to each subject's body weight (BW), RESULTS -For the male subjects the mean peak vertical force range for alt shoes was 2.9 -3,OBW, impact force 2,5 -2.8BW, braking 0.62 -0.70BW, and propulsive OAO -OA4BW. For the females the mean peak range was vertical force 2.75 -2.78BW, impact force 2.1 -2.5BW, braking 0.57 -0.59BW, and propulsive 0.37 -0.41 BW. In both the male and female subjects a low mean peak braking force and low mean peak vertical impact force was associated with a high mean peak propulsive force (male: Adidas Tech Performance Braking 0.616BW, Impact 2.531 BW, Propulsive OA43BW; female: Adidas Response Lite Braking 0.572BW, Impact 2.072BW, Propulsive OA09BW). Similarly a high mean peak braking force and high mean peak impact force was associated with a low mean peak propulsive force (male: Puma Disc system TX4000 Braking 0.700BW, Impact 2.768BW, Propulsive OA02BW; female: Adidas Lady Tech Performance Braking 0.591 BW, Impact 2A82BW, Propulsive 0 379BW). Differences were significant (P < 005) CONCLUSION -For two shoe designs the existence of a lower vertical impact force and low braking force is associated with greater propulsive force

Triple-horizon spherically symmetric spacetime and holographic principle

We present a family of spherically symmetric spacetimes, specified by the density profile of a vacuum dark energy, which have the same global structure as the de Sitter spacetime but the reduced symmetry which leads to a time-evolving and spatially inhomogeneous cosmological term. It connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. This family contains a special class distinguished by dynamics of evaporation of a cosmological horizon which evolves to the triple horizon with the finite entropy, zero temperature, zero curvature, infinite positive specific heat, and infinite scrambling time. Non-zero value of the cosmological constant in the triple-horizon spacetime is tightly fixed by quantum dynamics of evaporation of the cosmological horizon.Comment: Honorable Mentioned Essay - Gravity Research Foundation 2012; submitted to Int. J. Mod. Phys.

Eigenvector localization for random band matrices with power law band width

It is shown that certain ensembles of random matrices with entries that vanish outside a band around the diagonal satisfy a localization condition on the resolvent which guarantees that eigenvectors have strong overlap with a vanishing fraction of standard basis vectors, provided the band width $W$ raised to a power $\mu$ remains smaller than the matrix size $N$. For a Gaussian band ensemble, with matrix elements given by i.i.d. centered Gaussians within a band of width $W$, the estimate $\mu \le 8$ holds.Comment: 30 pages; corrected typo