Integrable and superintegrable systems with spin

A system of two particles with spin s=0 and s=1/2 respectively, moving in a plane is considered. It is shown that such a system with a nontrivial spin-orbit interaction can allow an 8 dimensional Lie algebra of first-order integrals of motion. The Pauli equation is solved in this superintegrable case and reduced to a system of ordinary differential equations when only one first-order integral exists.Comment: 12 page

Elemental technetium as a cosmic-ray clock

Several radioactive isotopes have been proposed as clocks for the study of the mean cosmic ray confinement time, T sub e. Measurements of Be-10 and Al-26 give a value for T sub e of about 10 Myr when one uses a leaky box cosmic ray propagation model. It is important to obtain additional measurements of T sub e from other radioactive isotopes in order to check whether the confinement is the same throughout the periodic table. The possible use of Tc (Z = 43) as a cosmic clock is investigated. Since all isotopes of Tc are radioactive, one might be able to group these isotopes and use the elemental abundance as a whole. The results of the calculations are somewhat inconclusive for two reasons. First, the beta + decay half lives of two of the Tc isotopes relevant to our calculation are not known. Second, the dependence of the Tc abundance on the mean confinement time is rather weak when one considers the number of events expected in 4 trays of plastic track detectors. However, a future, finite measurement of the Beta + half lives and the possible use of the entire collecting area of the HNC to detect Tc nuclei could make the use of Tc as a cosmic ray clock more attractive

Addition theorems and the Drach superintegrable systems

We propose new construction of the polynomial integrals of motion related to the addition theorems. As an example we reconstruct Drach systems and get some new two-dimensional superintegrable Stackel systems with third, fifth and seventh order integrals of motion.Comment: 18 pages, the talk given on the conference "Superintegrable Systems in Classical and Quantum Mechanics", Prague 200

Integration of a generalized H\'enon-Heiles Hamiltonian

The generalized H\'enon-Heiles Hamiltonian $H=1/2(P_X^2+P_Y^2+c_1X^2+c_2Y^2)+aXY^2-bX^3/3$ with an additional nonpolynomial term $\mu Y^{-2}$ is known to be Liouville integrable for three sets of values of $(b/a,c_1,c_2)$. It has been previously integrated by genus two theta functions only in one of these cases. Defining the separating variables of the Hamilton-Jacobi equations, we succeed here, in the two other cases, to integrate the equations of motion with hyperelliptic functions.Comment: LaTex 2e. To appear, Journal of Mathematical Physic

From strange to charmed baryons using two-flavour QCD

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Nambu-Jona-Lasinio model with Wilson fermions

12 pages, 5 figuresWe present a lattice study of a Nambu Jona-Lasinio (NJL) model using Wilson fermions. Four fermion interactions are a natural part of several extensions of the Standard Model, appearing as a low energy description of a more fundamental theory. In models of dynamical electroweak symmetry breaking they are used to endow the Standard Model fermions with masses. In infrared conformal models these interaction, when sufficiently strong, can alter the dynamics of the fixed point, turning the theory into a (near) conformal model with desirable features for model building. As a first step toward the nonperturbative study of these models, we study the phase space of the ungauged NJL model

Third-order superintegrable systems separable in parabolic coordinates

In this paper, we investigate superintegrable systems which separate in parabolic coordinates and admit a third-order integral of motion. We give the corresponding determining equations and show that all such systems are multi-separable and so admit two second-order integrals. The third-order integral is their Lie or Poisson commutator. We discuss how this situation is different from the Cartesian and polar cases where new potentials were discovered which are not multi-separable and which are expressed in terms of Painlev\'e transcendents or elliptic functions

The effects of pressure, nozzle diameter and meteorological conditions on the performance of agricultural impact sprinklers

19 Pags. The definitive version, with Figs. y Tabls., is available at: http://www.sciencedirect.com/science/journal/03783774This study evaluates agricultural impact sprinklers under different combinations of pressure (p), nozzle diameter (D) and meteorological conditions. The radial curve (Rad) of an isolated sprinkler, i.e., the water distribution along the wetted radius, was evaluated through 25 tests. Christiansen's uniformity coefficient (CUC) and the wind drift and evaporation losses (WDEL) were evaluated for a solid-set system using 52 tests. The Rad constitutes the footprint of a sprinkler. The CUC is intimately connected to the Rad. The Rad must be characterized under calm conditions. Very low winds, especially prevailing winds, significantly distort the water distribution. The vector average of the wind velocity (V’) is recommended as a better explanatory variable than the more popular arithmetic average (V). We recommend characterizing the Rad under indoor conditions or under conditions that meet V’ < 0.6 m s−1 in open-air conditions. The Rad was mostly affected by the sprinkler model. V’ was the main explanatory variable for the CUC; p was significant as well. V was the main variable explaining the WDEL; the air temperature (T) was significant, too. Sprinkler irrigation simulators simplify the selection of a solid-set system for farmers, designers and advisors. However, the quality of the simulations greatly depends on the characterization of the Rad. This work provides useful recommendations in this area.This research was funded by the Government of Spain through grants AGL2004-06675-C03-03/AGR, AGL2007-66716-C03 and AGL2010-21681, by the Government of Aragón through grant PIP090/2005, and by the INIA and CITA through the PhD grants program.Peer reviewe