Analytical results for the confinement mechanism in QCD_3

We present analytical methods for investigating the interaction of two heavy quarks in QCD_3 using the effective action approach. Our findings result in explicit expressions for the static potentials in QCD_3 for long and short distances. With regard to confinement, our conclusion reflects many features found in the more realistic world of QCD_4.Comment: 24 pages, uses REVTe

Quaternions, octonions and Bell-type inequalities

Multipartite Bell-type inequalities are derived for general systems. They involve up to eight observables with arbitrary spectra on each site. These inequalities are closely related to the algebras of quaternions and octonions.Comment: 4 pages, no figure

High Temperature Expansion Study of the Nishimori multicritical Point in Two and Four Dimensions

We study the two and four dimensional Nishimori multicritical point via high temperature expansions for the $\pm J$ distribution, random-bond, Ising model. In $2d$ we estimate the the critical exponents along the Nishimori line to be $\gamma=2.37\pm 0.05$, $\nu=1.32\pm 0.08$. These, and earlier $3d$ estimates $\gamma =1.80\pm 0.15$, $\nu=0.85\pm 0.08$ are remarkably close to the critical exponents for percolation, which are known to be $\gamma=43/18$, $\nu=4/3$ in $d=2$ and $\gamma=1.805\pm0.02$ and $\nu=0.875\pm 0.008$ in $d=3$. However, the estimated $4d$ Nishimori exponents $\gamma=1.80\pm 0.15$, $\nu=1.0\pm 0.1$, are quite distinct from the $4d$ percolation results $\gamma=1.435\pm 0.015$, $\nu=0.678\pm 0.05$.Comment: 5 pages, RevTex, 3 postscript files; To appear in Physical Review

Billiard algebra, integrable line congruences, and double reflection nets

The billiard systems within quadrics, playing the role of discrete analogues of geodesics on ellipsoids, are incorporated into the theory of integrable quad-graphs. An initial observation is that the Six-pointed star theorem, as the operational consistency for the billiard algebra, is equivalent to an integrabilty condition of a line congruence. A new notion of the double-reflection nets as a subclass of dual Darboux nets associated with pencils of quadrics is introduced, basic properies and several examples are presented. Corresponding Yang-Baxter maps, associated with pencils of quadrics are defined and discussed.Comment: 18 pages, 8 figure

A Mathematical Theory of Stochastic Microlensing II. Random Images, Shear, and the Kac-Rice Formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (p.d.f.) of the random shear tensor at a general point in the lens plane due to point masses in the limit of an infinite number of stars. Up to this order, the p.d.f. depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the stars' masses. As a consequence, the p.d.f.s of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic p.d.f. of the shear magnitude in the limit of an infinite number of stars is also presented. Extending to general random distributions of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of {\it global} expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars.Comment: To appear in JM

On the Electromagnetic Properties of Matter in Collapse Models

We discuss the electromagnetic properties of both a charged free particle, and a charged particle bounded by an harmonic potential, within collapse models. By choosing a particularly simple, yet physically relevant, collapse model, and under only the dipole approximation, we are able to solve the equation of motion exactly. In this way, both the finite time and large time behavior can be analyzed accurately. We discovered new features, which did not appear in previous works on the same subject. Since, so far, the spontaneous photon emission process places the strongest upper bounds on the collapse parameters, our results call for a further analysis of this process for those atomic systems which can be employed in experimental tests of collapse models, as well as of quantum mechanics.Comment: 17 pages, LaTeX, updated version with minor change

From Newton's Laws to the Wheeler-DeWitt Equation

This is a pedagogical paper which explains some ideas in cosmology at a level accessible to undergraduate students. It does not use general relativity, but uses the ideas of Newtonian cosmology worked out by Milne and McCrea. The cosmological constant is also introduced within a Newtonian framework. Following standard quantization procedures the Wheeler-DeWitt equation in the minisuperspace approximation is derived for empty and non-empty universes.Comment: 13 pages, 1 figur

CELLULAR RECOGNITION IN VITRO BY MOUSE LYMPHOCYTES : EFFECTS OF NEONATAL THYMECTOMY AND THYMUS GRAFT RESTORATION ON ALLOANTIGEN AND PHA STIMULATION OF WHOLE AND GRADIENT-SEPARATED SUBPOPULATIONS OF SPLEEN CELLS

The effects of thymectomy and thymus graft restoration upon the in vitro primary responses to alloantigens and PHA have been studied. It has been found that neonatal thymectomy substantially eliminates both PHA reactivity and responsiveness to alloantigens assayed in vitro in host spleen cell populations. Analysis of albumin density gradient-separated subpopulations of the spleen and thymus in such animals was also performed. It was found that the total and proportional representation of the individual density subpopulations was identical in neonatally thymectomized, in normal, and in thymectomized and thymus graft-restored animals. Therefore, thymectomized mice appear to retain a nonfunctioning, small, dense, lymphocyte population. Reconstitution of thymic-dependent in vitro reactivity was nearly complete when syngeneic, but not allogeneic or semisyngeneic thymus was employed. Occasional partial restoration did occur when F1 thymus was employed, but never when allogeneic thymus was grafted. The grafted thymus contained PHA and alloantigen-reactive cells in a large, less dense B layer subpopulation, whereas the restored animals, as in the case of normals, showed these reactivities to be a property of a small, more dense cell population

Chaos and Beyond in a Water Filled Ultrasonic Resonance System

Finite amplitude ultrasonic wave resonances in a one-dimensional liquid-filled cavity, formed by a narrow band transducer and a plane reflector, are reported. The resonances are observed to include not only the expected harmonic and subharmonic signals (1,2) but chaotic signals as well. The generation mechanism requires attaining a threshold value of the driving amplitude that the liquid-filled cavity system becomes sufficiently nonlinear in response. The nonlinear features of the system were recently investigated via the construction of an ultrasonic interferometer having optical precision. The transducers were compressional, undamped quartz and lithium niobate crystals having the frequency range 1-10 MHz, driven by a high power amplifier. Both an optical diffraction system to characterize the diffraction pattern of laser light normally incident to the cavity and a receiving transducer attached to an aligned reflector with lapped flat and parallel surfaces were used to assess the generated resonance response in the cavity. At least 5 regions of excitation are identified