Versal deformations of a Dirac type differential operator

If we are given a smooth differential operator in the variable $x\in {\mathbb R}/2\pi {\mathbb Z},$ its normal form, as is well known, is the simplest form obtainable by means of the \mbox{Diff}(S^1)-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced \mbox{Diff}(S^1)-actions endowed with centrally extended Lie-Poisson brackets. After constructing a general expression for tranversal deformations of a Dirac type differential operator, we interpret it via the Lie-algebraic theory of induced \mbox{Diff}(S^1)-actions on a special Poisson manifold and determine its generic moment mapping. Using a Marsden-Weinstein reduction with respect to certain Casimir generated distributions, we describe a wide class of versally deformed Dirac type differential operators depending on complex parameters

The restricted two-body problem in constant curvature spaces

We perform the bifurcation analysis of the Kepler problem on $S^3$ and $L^3$. An analogue of the Delaunay variables is introduced. We investigate the motion of a point mass in the field of the Newtonian center moving along a geodesic on $S^2$ and $L^2$ (the restricted two-body problem). When the curvature is small, the pericenter shift is computed using the perturbation theory. We also present the results of the numerical analysis based on the analogy with the motion of rigid body.Comment: 29 pages, 7 figure

Duality properties of indicatrices of knots

The bridge index and superbridge index of a knot are important invariants in knot theory. We define the bridge map of a knot conformation, which is closely related to these two invariants, and interpret it in terms of the tangent indicatrix of the knot conformation. Using the concepts of dual and derivative curves of spherical curves as introduced by Arnold, we show that the graph of the bridge map is the union of the binormal indicatrix, its antipodal curve, and some number of great circles. Similarly, we define the inflection map of a knot conformation, interpret it in terms of the binormal indicatrix, and express its graph in terms of the tangent indicatrix. This duality relationship is also studied for another dual pair of curves, the normal and Darboux indicatrices of a knot conformation. The analogous concepts are defined and results are derived for stick knots.Comment: 22 pages, 9 figure

Analytical solutions for two heteronuclear atoms in a ring trap

We consider two heteronuclear atoms interacting with a short-range $\delta$ potential and confined in a ring trap. By taking the Bethe-ansatz-type wavefunction and considering the periodic boundary condition properly, we derive analytical solutions for the heteronuclear system. The eigen-energies represented in terms of quasi-momentums can then be determined by solving a set of coupled equations. We present a number of results, which display different features from the case of identical atoms. Our result can be reduced to the well-known Lieb-Liniger solution when two interacting atoms have the same masses.Comment: 6 pages, 6 figure

Semirigid Geometry

We provide an intrinsic description of $N$-super \RS s and $TN$-\SR\ surfaces. Semirigid surfaces occur naturally in the description of topological gravity as well as topological supergravity. We show that such surfaces are obtained by an integrable reduction of the structure group of a complex supermanifold. We also discuss the \s moduli spaces of $TN$-\SR\ surfaces and their relation to the moduli spaces of $N$-\s\ \RS s.Comment: 29p

Limits on different Majoron decay modes of 100^{100}Mo and 82^{82}Se for neutrinoless double beta decays in the NEMO-3 experiment

The NEMO-3 tracking detector is located in the Fr\'ejus Underground Laboratory. It was designed to study double beta decay in a number of different isotopes. Presented here are the experimental half-life limits on the double beta decay process for the isotopes $^{100}$Mo and $^{82}$Se for different Majoron emission modes and limits on the effective neutrino-Majoron coupling constants. In particular, new limits on "ordinary" Majoron (spectral index 1) decay of $^{100}$Mo ($T_{1/2} > 2.7\cdot10^{22}$ y) and $^{82}$Se ($T_{1/2} > 1.5\cdot10^{22}$ y) have been obtained. Corresponding bounds on the Majoron-neutrino coupling constant are $< (0.4-1.9) \cdot 10^{-4}$ and $< (0.66-1.7) \cdot 10^{-4}$.Comment: 23 pages includind 4 figures, to be published in Nuclear Physics

Recent advances in neutrinoless double beta decay search

Even after the discovery of neutrino flavour oscillations, based on data from atmospheric, solar, reactor, and accelerator experiments, many characteristics of the neutrino remain unknown. Only the neutrino square-mass differences and the mixing angle values have been estimated, while the value of each mass eigenstate still hasn't. Its nature (massive Majorana or Dirac particle) is still escaping. Neutrinoless double beta decay ($0\nu$-DBD) experimental discovery could be the ultimate answer to some delicate questions of elementary particle and nuclear physics. The Majorana description of neutrinos allows the $0\nu$-DBD process, and consequently either a mass value could be measured or the existence of physics beyond the standard should be confirmed without any doubt. As expected, the $0\nu$-DBD measurement is a very difficult field of application for experimentalists. In this paper, after a short summary of the latest results in neutrino physics, the experimental status, the R&D projects, and perspectives in $0\nu$-DBD sector are reviewed.Comment: 36 pages, 7 figures, To be publish in Czech Journal of Physic

Superfluid toroidal currents in atomic condensates

The dynamics of toroidal condensates in the presence of condensate flow and dipole perturbation have been investigated. The Bogoliubov spectrum of condensate is calculated for an oblate torus using a discrete-variable representation and a spectral method to high accuracy. The transition from spheroidal to toroidal geometry of the trap displaces the energy levels into narrow bands. The lowest-order acoustic modes are quantized with the dispersion relation $\omega \sim |m| \omega_s$ with $m=0,\pm 1,\pm 2, ...$. A condensate with toroidal current $\kappa$ splits the $|m|$ co-rotating and counter-rotating pair by the amount: $\Delta E \approx 2 |m|\hbar^2 \kappa < r^{-2}>$. Radial dipole excitations are the lowest energy dissipation modes. For highly occupied condensates the nonlinearity creates an asymmetric mix of dipole circulation and nonlinear shifts in the spectrum of excitations so that the center of mass circulates around the axis of symmetry of the trap. We outline an experimental method to study these excitations.Comment: 8 pages, 8 figure

Non-abelian plane waves and stochastic regimes for (2+1)-dimensional gauge field models with Chern-Simons term

An exact time-dependent solution of field equations for the 3-d gauge field model with a Chern-Simons (CS) topological mass is found. Limiting cases of constant solution and solution with vanishing topological mass are considered. After Lorentz boost, the found solution describes a massive nonlinear non-abelian plane wave. For the more complicate case of gauge fields with CS mass interacting with a Higgs field, the stochastic character of motion is demonstrated.Comment: LaTeX 2.09, 13 pages, 11 eps figure

Search for β+\beta^+EC and ECEC processes in 112^{112}Sn and β−β−\beta^-\beta^- decay of 124^{124}Sn to the excited states of 124^{124}Te

Limits on $\beta^+$EC and ECEC processes in $^{112}$Sn and on $\beta^-\beta^-$ decay of $^{124}$Sn to the excited states of $^{124}$Te have been obtained using a 380 cm$^3$ HPGe detector and an external source consisting of natural tin. A limit with 90% C.L. on the $^{112}$Sn half-life of $0.92\times 10^{20}$ y for the ECEC(0$\nu$) transition to the $0^+_3$ excited state in $^{112}$Cd (1871.0 keV) has been established. This transition is discussed in the context of a possible enhancement of the decay rate by several orders of magnitude given that the ECEC$(0\nu)$ process is nearly degenerate with an excited state in the daughter nuclide. Prospects for investigating such a process in future experiments are discussed. The $\beta^-\beta^-$ decay limits for $^{124}$Sn to the excited states of $^{124}$Te were obtained on the level of $(0.8-1.2)\times 10^{21}$ y at the 90% C.L.Comment: 17 pages, 5 figure