Nitrogen Trichloride with Benzalacetophenone

Nitrogen trichloride and benzalacetophenone in carbon tetrachloride solution between 20° and -15 ° react to form free nitrogen, ammonium chloride, benzalacetophenone dichloride, and a C-chloro-N -dichloroamino ketone. This compound can be reduced to the C-chloroamino ketone by means of concentrated hydrochloric acid. The hydrochloride and the benzoyl derivative of this compound were isolated and analyzed

Heavy Quark Potential from Gauge/Gravity Duality: A Large D Analysis

The heavy-quark potential is calculated in the framework of gauge/gravity duality using the large-D approximation, where D is the number of dimensions transverse to the flux tube connecting a quark and an antiquark in a flat D+2-dimensional spacetime. We find that in the large-D limit the leading correction to the ground-state energy, as given by an effective Nambu-Goto string, arises not from the heavy modes but from the behavior of the massless modes in the vicinity of the quark and the antiquark. We estimate this correction and find that it should be visible in the near-future lattice QCD calculations of the heavy-quark potential.Comment: 22 pages, 5 Figures. v2: references added, typos corrected and, Sec. 4 rewritten with an expanded non-perturbative discussion of the corrections to the Arvis potential arising from the massless modes near the boundary of the qcd strin

Chabauty-Coleman experiments for genus 3 hyperelliptic curves

We describe a computation of rational points on genus 3 hyperelliptic curves $C$ defined over $\mathbb{Q}$ whose Jacobians have Mordell-Weil rank 1. Using the method of Chabauty and Coleman, we present and implement an algorithm in Sage to compute the zero locus of two Coleman integrals and analyze the finite set of points cut out by the vanishing of these integrals. We run the algorithm on approximately 17,000 curves from a forthcoming database of genus 3 hyperelliptic curves and discuss some interesting examples where the zero set includes global points not found in $C(\mathbb{Q})$.Comment: 18 page

Probing the Planck Scale with Neutrino Oscillations

Quantum gravity "foam", among its various generic Lorentz non-invariant effects, would cause neutrino mixing. It is shown here that, if the foam is manifested as a nonrenormalizable effect at scale M, the oscillation length generically decreases with energy $E$ as (E/M)^(-2). Neutrino observatories and long-baseline experiments should have therefore already observed foam-induced oscillations, even if M is as high as the Planck energy scale. The null results, which can be further strengthened by better analysis of current data and future experiments, can be taken as experimental evidence that Lorentz invariance is fully preserved at the Planck scale, as is the case in critical string theory.Comment: 11 pages, 2 figures. Final version published in PRD. 1 figure, references, clarifications and explanations added. Results unchange

Significant Conditions on the Two-electron Reduced Density Matrix from the Constructive Solution of N-representability

We recently presented a constructive solution to the N-representability problem of the two-electron reduced density matrix (2-RDM)---a systematic approach to constructing complete conditions to ensure that the 2-RDM represents a realistic N-electron quantum system [D. A. Mazziotti, Phys. Rev. Lett. 108, 263002 (2012)]. In this paper we provide additional details and derive further N-representability conditions on the 2-RDM that follow from the constructive solution. The resulting conditions can be classified into a hierarchy of constraints, known as the (2,q)-positivity conditions where the q indicates their derivation from the nonnegativity of q-body operators. In addition to the known T1 and T2 conditions, we derive a new class of (2,3)-positivity conditions. We also derive 3 classes of (2,4)-positivity conditions, 6 classes of (2,5)-positivity conditions, and 24 classes of (2,6)-positivity conditions. The constraints obtained can be divided into two general types: (i) lifting conditions, that is conditions which arise from lifting lower (2,q)-positivity conditions to higher (2,q+1)-positivity conditions and (ii) pure conditions, that is conditions which cannot be derived from a simple lifting of the lower conditions. All of the lifting conditions and the pure (2,q)-positivity conditions for q>3 require tensor decompositions of the coefficients in the model Hamiltonians. Subsets of the new N-representability conditions can be employed with the previously known conditions to achieve polynomially scaling calculations of ground-state energies and 2-RDMs of many-electron quantum systems even in the presence of strong electron correlation

A deep Large Binocular Telescope view of the Canes Venatici I dwarf galaxy

We present the first deep color-magnitude diagram of the Canes Venatici I (CVnI) dwarf galaxy from observations with the wide field Large Binocular Camera on the Large Binocular Telescope. Reaching down to the main-sequence turnoff of the oldest stars, it reveals a dichotomy in the stellar populations of CVnI: it harbors an old (> 10 Gyr), metal-poor ([Fe/H] ~ -2.0) and spatially extended population along with a much younger (~ 1.4-2.0 Gyr), 0.5 dex more metal-rich, and spatially more concentrated population. These young stars are also offset by 64_{-20}^{+40} pc to the East of the galaxy center. The data suggest that this young population, which represent ~ 3-5 % of the stellar mass of the galaxy within its half-light radius, should be identified with the kinematically cold stellar component found by Ibata et al. (2006). CVnI therefore follows the behavior of the other remote MW dwarf spheroidals which all contain intermediate age and/or young populations: a complex star formation history is possible in extremely low-mass galaxies.Comment: 4 pages, 3 figures, accepted for publication in ApJL. Minor changes, conclusions unchange

The Exact Critical Bubble Free Energy and the Effectiveness of Effective Potential Approximations

To calculate the temperature at which a first-order cosmological phase transition occurs, one must calculate $F_c(T)$, the free energy of a critical bubble configuration. $F_c(T)$ is often approximated by the classical energy plus an integral over the bubble of the effective potential; one must choose a method for calculating the effective potential when $V''<0$. We test different effective potential approximations at one loop. The agreement is best if one pulls a factor of $\mu^4/T^4$ into the decay rate prefactor [where $\mu^2 = V''(\phi_f)$], and takes the real part of the effective potential in the region $V''<0$. We perform a similar analysis on the 1-dimensional kink.Comment: 11 pages plus 3 figures in jyTeX; CALT-68-188

On touching random surfaces, two-dimensional quantum gravity and non-critical string theory

A set of physical operators which are responsible for touching interactions in the framework of c<1 unitary conformal matter coupled to 2D quantum gravity is found. As a special case the non-critical bosonic strings are considered. Some analogies with four dimensional quantum gravity are also discussed, e.g. creation-annihilation operators for baby universes, Coleman mechanism for the cosmological constant.Comment: 22 pages, Latex2e, 3 figure