On General Plane Fronted Waves. Geodesics

A general class of Lorentzian metrics, , , with any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity causal character of connecting geodesics. These results are independent of the possibility of a full integration of geodesic equations. Variational and geometrical techniques are applied systematically. In particular, we prove that the asymptotic behavior of H(x,u) with x at infinity determines many properties of geodesics. Essentially, a subquadratic growth of H ensures geodesic completeness and connectedness, while the critical situation appears when H(x,u) behaves in some direction as , as in the classical model of exact gravitational waves.     

Measurement of inclusive Λ production in electron-positron interactions at the upsilon energies

Using the MD-1 detector at the VEPP-4e ⁺ e ^– strorage ring we have measured the inclusive and370-1 production rates in direct (1S) decays

The role of the induced currents in the mass mechanism of neutrinoless double-beta decay

The nuclear matrix elements of Majorana neutrino mass mechanism of neutrinoless double-beta decay have so far been calculated using only contributions from vector axial-vector part and weak magnetism of the nuclear current, while other contributions have been neglected. In the present work we are examining the effect of weak magnetism and induced pseudoscalar coupling. We have performed calculations within the proton-neutron renormalized quasiparticle random phase approximation and we have found that these additional contributions of the nucleon current, result in a considerable reduction of the nuclear matrix elements of all nuclei which we have considered. This reduction of the nuclear matrix element makes the extracted limits of the lepton number violating parameters less stringent yielding the best value for less than 0.51 eV for ⁷⁶Ge.     

NMRON studies of MnBr2 \cdot 4H2O in applied magnetic fields

NMRON studies for the ⁵⁴Mn transitions in antiferromagnetic MnBr₂ 4H₂O, in the millikelvin regime, are presented and discussed. New values are given for (i) the sum of the effective molecular exchange and magnetic anisotropy fields acting on the Mn²⁺ ions, =2.23(2) T, and (ii) the magnetic dipole hyperfine splitting, A=-201.99(1) MHz, electric quadrupole hyperfine splitting P=0.049(8) MHz and pseudoquadrupole splitting =1.63(2) MHz for the ⁵⁴Mn nuclei.     

On the Modified Korteweg–De Vries Equation

We consider the large time asymptotic behavior of solutions to the Cauchy problem for the modified Korteweg–de Vries equation , with initial data . We assume that the coefficient is real, bounded and slowly varying function, such that , where . We suppose that the initial data are real-valued and small enough, belonging to the weighted Sobolev space . In comparison with the previous paper (Internat. Res. Notices 8 (1999), 395–418), here we exclude the condition that the integral of the initial data u ₀ is zero. We prove the time decay estimates and for all , where . We also find the asymptotics for large time of the solution in the neighborhood of the self-similar solution.     

Intersections in Genus 3 and the Boussinesq Hierarchy

In this Letter we prove that the enlarged Witten conjecture is true in the case of the Boussinesq hierarchy for correlators .     

Diffusion in a symmetric bistable potential: A variational approach

An approximation procedure for the solution of stochastic nonlinear equations, which was derived from a variational principle in a previous paper, is applied to the problem of a particle that diffuses in a symmetric bistable potential starting from the point of unstable equilibrium. The second moment and variance for the particle's position are calculated as functions of the timet. Good agreement is found with results recently obtained by Baibuzet al. from an approximate evaluation of a path integral expression for the probability density.     

Search for double electron capture of 106Cd

A search for double electron capture of ¹⁰⁶Cd was performed at the Modane Underground Laboratory (4800 m w.e.) using a low-background and high-sensitivity multidetector spectrometer TGV-2 (Telescope Germanium Vertical). New limits on β ⁺/EC, EC/EC decays of ¹⁰⁶Cd were obtained from preliminary calculations of experimental data accumulated for 4800 h of measurement of 10 g of ¹⁰⁶Cd with enrichment of 75%. They are > 9.1 × 10¹⁸ yr, > 1.9 × 10¹⁹ yr for transitions to the first 2⁺, 511.9 keV excited state of ¹⁰⁶Pd, and > 1.3 × 10¹⁹ yr, > 6.2 × 10¹⁹ yr for transitions to the ground 0⁺ state of ¹⁰⁶Pd. All limits are given at 90% C.L. The text was submitted by the authors in English.     

Preferred Invariant Symplectic Connections on Compact Coadjoint Orbits

Let be the Haag--Kastler net generated by the (2) chiral current algebra at level 1. We classify the SL(2, )-covariant subsystems by showing that they are all fixed points nets ^H for some subgroup H of the gauge automorphisms group SO(3) of . Then, using the fact that the net ₁ generated by the (1) chiral current can be regarded as a subsystem of , we classify the subsystems of ₁. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem .     

On the Product of Real Spectral Triples

The product of two real spectral triples and , the first of which is necessarily even, was defined by A.Connes as given by and, in the even-even case, by . Generically it is assumed that the real structure obeys the relations , , , where the -sign table depends on the dimension n modulo 8 of the spectral triple. If both spectral triples obey Connes' >-sign table, it is seen that their product, defined in the straightforward way above, does not necessarily obey this -sign table. In this Letter, we propose an alternative definition of the product real structure such that the -sign table is also satisfied by the product.     

Transport Properties of Kicked and Quasiperiodic Hamiltonians

We study transport properties of Schrödinger operators depending on one or more parameters. Examples include the kicked rotor and operators with quasi-periodic potentials. We show that the mean growth exponent of the kinetic energy in the kicked rotor and of the mean square displacement in quasiperiodic potentials is generically equal to 2: this means that the motion remains ballistic, at least in a weak sense, even away from the resonances of the models. Stronger results are obtained for a class of tight-binding Hamiltonians with an electric field E(t) = E ₀+ E ₁cos t. For with 3/2)$$ " align="middle" border="0"> we show that the mean square displacement satisfies for suitable choices of , E ₀, and E ₁. We relate this behavior to the spectral properties of the Floquet operator of the problem.     

Symmetry breaking in Landau gauge a comment to a paper by T. Kennedy and C. King

For the non-compact abelian lattice Higgs model in Landau gauge Kennedy and King (Princeton preprint, 1985) showed that the two point function does not decay in the Higgs phase. We generalize their methods to show that for the same range of parameters there are states parametrized by an angle [0, 2) such that and 0$$ " align="middle" border="0"> .     

Using the e ± μ? + E Tmiss signature in the search for supersymmetry and lepton-flavor violation in neutralino decays

The LHC (CMS) discovery potential in the search for supersymmetry and lepton-flavor violation in neutralino decays using the e ^± μ^∓ + E _T ^miss signature is studied. A detailed study is done for the CMS test points LM1-LM9. It is shown that, for the point LM1, it is possible to detect lepton-flavor violation in neutralino decays with lepton-flavor-violating branching Br( → μ^± e ^∓ ) ≥ 0.04 Br( → e ⁺ e ⁻ , μ⁺ μ⁻ ) for an integral luminosity of 10 fb⁻¹. The discovery potential in the mSUGRA-SUSY scenario with tan β = 10, sgn(μ) = + in the (m ₀, m _1/2) plane using the e ^± μ^∓ + E _T ^miss signature is determined. The text was submitted by the authors in English.     

Decay of two-point functions for (d+1)-dimensional percolation,ising and Potts models withd-dimensional disorder

Let and be independent sets of nonnegative i.i.d.r.v.'s, <x,y> denoting a pair of nearest neighbors inZ ^d; let , >0. We consider the random systems: 1. A bond Bernoulli percolation model onZ ^d+1 with random occupation probabilities     

On the Yangian Y $$(\mathfrak{g}\mathfrak{l}_{m|n} )$$ and its quantum Berezinian

Jonathan Brundan and Alexander Kleshchev recently introduced a new family of presentations for the Yangian Y of the general linear Lie algebra . In this article, we extend some of their ideas to consider the Yangian Y of the Lie superalgebra . In particular, we give a new proof of the result by Nazarov that the quantum Berezinian is central. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

CP -violation effects in the decays B ? → D * K *? and method for determining the weak phase γ

A method for determining the angle γ and the ratio of the amplitudes A _λ(B ⁻ → K ^*−) and A _λ)B ⁻ → D ^*0 K ^*−), r _Bλ, for all three vector-meson polarization states by using the decays B ^∓ → D ^* K ^*∓ is proposed. This method relies on the interference between the decays B ⁻ → D ^*0 K ^*− and B ⁻ → K ^*−, which arises if D ^*0 and decay to D ⁰/ π ⁰ and D ⁰/ γ, whereupon D ⁰ and mesons decay to common final hadron states. The doubly Cabibbo-suppressed modes of D ⁰-meson decay are chosen here to specify such final states. Original Russian Text ? V.A. Kovalchuk, 2007, published in Yadernaya Fizika, 2007, Vol. 70, No. 4, pp. 754–763.     

Bounds on neutrino mixing with exotic singlet neutrinos

We examine the effects of mixing induced non-diagonal light-heavy neutrino weak neutral currents on the amplitude for the process (with a=e, μ or τ). By imposing constraint that the amplitude should not exceed the perturbative unitarity limit at high energy , we obtain bounds on light-heavy neutrino mixing parameter sin² where is the mixing angle. In the case of one heavy neutrino (mass mξ) or mass degenerate heavy neutrinos, for Λ=1 TeV, no bound is obtained for mξ<0.50 TeV. However, sin² ≤3.8 × 10⁻⁶ for mξ=5 TeV and sin ≤6.0 × 10⁻⁸ for mξ=10 TeV. For Λ=∞, no constraint is obtained for mξ<0.99 TeV and sin² ≤3.8 × 10⁻² (for mξ=5 TeV) and sin² ≤9.6 × 10⁻³ (for mξ=10 TeV).     

Covariant (hh′)-Deformed Bosonic and Fermionic Algebras as Contraction Limits of q-Deformed Ones

GL_h(n) ×GL_h(m)-covariant (hh)-bosonic[or (hh)-fermionic] algebras are built in terms of thecorresponding R_h and -matrices by contracting theGL_q(n) × -covariant q-bosonic (or q-fermionic) algebras , = 1, 2.When using a basis of wherein theannihilation operators are contragredient to thecreation ones, this contraction procedure can be carried out for any n, m values. Whenemploying instead a basis wherein the annihilationoperators, like the creation ones, are irreducibletensor operators with respect to the dual quantumalgebra U_q(gl(n)) , a contraction limit only exists forn, m {1, 2, 4, 6, . . .}. For n = 2, m = 1, andn = m = 2, the resulting relations can be expressed interms of coupled (anti)commutators (as in the classical case), by usingU_h(sl(2)) [instead of s1(2)] Clebsch-Gordancoefficients. Some U_h(sl(2)) rank-1/2irreducible tensor operators recently constructed byAizawa are shown to provide a realization of (2, 1).     

Symmetries and Modular Intersections of Von Neumann Algebras

Let be von Neumann algebras acting on a Hilbert space and let be a common cyclic and separating vector. We say that have the modular intersection property with respect to if(1) -half-sided modular inclusions,(2) (If (1) holds the strong limit exists.) We show that under these conditions the modular groups of and generate a 2-dim. Lie group.This observation is the basis for obtaining group representations of Sl(2, )/Z ₂ generated by modular groups.