Perspectives on Nuclear Structure and Scattering with the Ab Initio No-Core Shell Model

Nuclear structure and reaction theory are undergoing a major renaissance with advances in many-body methods, strong interactions with greatly improved links to Quantum Chromodynamics (QCD), the advent of high performance computing, and improved computational algorithms. Predictive power, with well-quantified uncertainty, is emerging from non-perturbative approaches along with the potential for new discoveries such as predicting nuclear phenomena before they are measured. We present an overview of some recent developments and discuss challenges that lie ahead. Our focus is on explorations of alternative truncation schemes in the harmonic oscillator basis, of which our Japanese--United States collaborative work on the No-Core Monte-Carlo Shell Model is an example. Collaborations with Professor Takaharu Otsuka and his group have been instrumental in these developments.Comment: 8 pages, 5 figures, accepted for publication in Proceedings of Perspectives of the Physics of Nuclear Structure, JPS Conference Proceedings, Japan (to appear

Exponents of 2-multiarrangements and multiplicity lattices

We introduce a concept of multiplicity lattices of 2-multiarrangements, determine the combinatorics and geometry of that lattice, and give a criterion and method to construct a basis for derivation modules effectively.Comment: 14 page

Stochastical distributions of lens and source properties for observed galactic microlensing events

A comprehensive new approach is presented for deriving probability densities of physical properties characterizing lens or source that constitute an observed galactic microlensing event. While previously encountered problems are overcome, constraints from event anomalies and model parameter uncertainties can be incorporated into the estimate. Probability densities for given events need to be carefully distinguished from the statistical distribution of the same parameters among the underlying population from which the actual lenses and sources are drawn. Using given model distributions of the mass spectrum, the mass density, and the velocity distribution of Galactic disk and bulge constituents, probability densities of lens mass, distance, and the effective lens-source velocities are derived, where the effect on the distribution that arises from additional observations of annual parallax or finite-source effects, or the absence of significant effects, is shown. The presented formalism can also be used to calculate probabilities for the lens to belong to one or another population and to estimate parameters that characterize anomalies. Finally, it is shown how detection efficiency maps for binary-lens companions in the physical parameters companion mass and orbital semi-major axis arise from values determined for the mass ratio and dimensionless projected separation parameter, including the deprojection of the orbital motion for elliptical orbits. Compared to the naive estimate based on 'typical values', the detection efficiency for low-mass companions is increased by mixing in higher detection efficiencies for smaller mass ratios (i.e. smaller masses of the primary).Comment: 25 pages with 22 embedded EPS-figures, uses mn2e.cls. Adopted mass function revised and one example event replaced, content rearranged, some minor changes. Submitted to MNRA

Tsallis Ensemble as an Exact Orthode

We show that Tsallis ensemble of power-law distributions provides a mechanical model of nonextensive equilibrium thermodynamics for small interacting Hamiltonian systems, i.e., using Boltzmann's original nomenclature, we prove that it is an exact orthode. This means that the heat differential admits the inverse average kinetic energy as an integrating factor. One immediate consequence is that the logarithm of the normalization function can be identified with the entropy, instead of the q-deformed logarithm. It has been noted that such entropy coincides with Renyi entropy rather than Tsallis entropy, it is non-additive, tends to the standard canonical entropy as the power index tends to infinity and is consistent with the free energy formula proposed in [S. Abe et. al. Phys. Lett. A 281, 126 (2001)]. It is also shown that the heat differential admits the Lagrange multiplier used in non-extensive thermodynamics as an integrating factor too, and that the associated entropy is given by ordinary nonextensive entropy. The mechanical approach proposed in this work is fully consistent with an information-theoretic approach based on the maximization of Renyi entropy.Comment: 5 pages. Added connection with Renyi entrop

Effects of initial compression stress on wave propagation in carbon nanotubes

An analytical method to investigate wave propagation in single- and double- walled carbon nanotubes under initial compression stress is presented. The nanotube structures are treated within the multilayer thin shell approximation with the elastic properties taken to be those of the graphene sheet. The governing equations are derived based on Flugge equations of motion. Frequency equations of wave propagation in single and double wall carbon nanotubes are described through the effects of initial compression stress and van der Waals force. To show the effects of Initial compression stress on the wave propagation in nanotubes, the symmetrical mode can be analyzed based on the present elastic continuum model. It is shown that the wave speed are sensitive to the compression stress especially for the lower frequencies.Comment: 12 pages, 4 figure

U-Spin Tests of the Standard Model and New Physics

Within the standard model, a relation involving branching ratios and direct CP asymmetries holds for the B-decay pairs that are related by U-spin. The violation of this relation indicates new physics (NP). In this paper, we assume that the NP affects only the Delta S = 1 decays, and show that the NP operators are generally the same as those appearing in B -> pi K decays. The fit to the latest B -> pi K data shows that only one NP operator is sizeable. As a consequence, the relation is expected to be violated for only one decay pair: Bd -> K0 pi0 and Bs -> Kbar0 pi0.Comment: 12 pages, latex, no figures. References changed to follow MPL guidelines; info added about U-spin breaking and small NP strong phases; discussion added about final-state pi-K rescattering; analysis and conclusions unaltere

Information measures based on Tsallis' entropy and geometric considerations for thermodynamic systems

An analysis of the thermodynamic behavior of quantum systems can be performed from a geometrical perspective investigating the structure of the state space. We have developed such an analysis for nonextensive thermostatistical frameworks, making use of the q-divergence derived from Tsallis' entropy. Generalized expressions for operator variance and covariance are considered, in terms of which the fundamental tensor is given.Comment: contribution to 3rd NEXT-SigmaPhi International Conference (August 2005, Kolymbari, Greece

Generalized entropies and the transformation group of superstatistics

Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$, where the `kernel' $f(\beta)$ is nonnegative and normalized ($\int f(\beta)d \beta =1$). We discuss the relation between this distribution and the generalized entropic form $S=\sum_i s(p_i)$. The first three Shannon-Khinchin axioms are assumed to hold. It then turns out that for a given distribution there are two different ways to construct the entropy. One approach uses escort probabilities and the other does not; the question of which to use must be decided empirically. The two approaches are related by a duality. The thermodynamic properties of the system can be quite different for the two approaches. In that connection we present the transformation laws for the superstatistical distributions under macroscopic state changes. The transformation group is the Euclidean group in one dimension.Comment: 5 pages, no figur

Scherk-Schwarz SUSY breaking from the viewpoint of 5D conformal supergravity

We reinterpret the Scherk-Schwarz (SS) boundary condition for SU(2)_R in a compactified five-dimensional (5D) Poincare supergravity in terms of the twisted SU(2)_U gauge fixing in 5D conformal supergravity. In such translation, only the compensator hypermultiplet is relevant to the SS twist, and various properties of the SS mechanism can be easily understood. Especially, we show the correspondence between the SS twist and constant superpotentials within our framework.Comment: 16 pages, no figur