On µ-symmetries, µ-reductions,and µ-conservation laws of Gardner equation

In this study, we represent an application of the geometrical characterization of µ-prolongations of vector fields to the nonlinear partial differential Gardner equation with variable coefficients. First, µ-symmetries and the corresponding µ-symmetry classification are investigated and then µ-reduction forms of the equations are obtained. Furthermore, µ-invariant solutions are determined and µ-conservation laws of Gardner equation are studied.     

Energetical structure of muonic molecular ions ddµ and dtµ

The long-lived states lying below then=2 threshold in muonic molecular ions ddµ and dtµ are reviewed. We have considered all the known long-lived states both of normal and anomalous spatial parity, the bound states as well as resonant three-body states of shape and Feshbach types. It is shown that these states could be satisfactorily classified in terms of the Born-Oppenheimer adiabatic theory. We calculate some characteristic properties of the Feshbach resonances, thus obtaining that the life-time of the 3d states is greater than 10^–11 s, and the fusion rate from these states less than 10⁹ s^–1. The geometry of the 4f(J=0,v=0) state shows that it does not obey approximate ungerade symmetry. On the contrary, the low vibrational 3d states are approximately of gerade symmetry, as a result these states decay ejecting dµ atoms in the same proportion as tµ atoms.     

µ -symmetry and µ -conservation law for the extended mKdV equation

In this paper, we obtain µ -symmetry and µ -conservation law of the extended mKdV equation. The extended mKdV equation dose not admit a variational problem since it is of odd order. First we obtain µ -conservation law of the extended mKdV equation in potential form because it admits a variational problem, using it, we can obtain µ -conservation law of the extended mKdV equation.     

New RIKEN-RAL pulsed µCF facility and X-ray studies on DT-µCF

In November 1994, the construction of a new superconducting muon channel of the RIKEN-RAL muon facility at ISIS of Rutherford Appleton Laboratory was completed. Subsequently, important features, such as the highest instantaneous intensity with a single-pulse structure and a high purity have been confirmed. Along with the installation of advanced µCF experimental equipment, including a high-purity D-T mixture target system with an in situ³He removal capability and a 4 T confinement magnet, an advanced µCF experiment, e.g. a precise X-ray measurement on µ- sticking in dtµ-µCF will be realized. An account of the commissioning experiments, a plan for the earliest phase of the µCF experiment and possible future directions are reported.     

Coulomb predissociation rates of He dµ molecular ions

The predissociation or particle emitting decay rates of muonic molecular ions³He dµ and⁴He dµ are estimated by means of the complex rotation method. We use a highly accurate variational three-bodyP-wave function based on random-tempered Slater-type exponential expansion. A resonance eigenvalue ofE=–48.420 89 eV and =0.348 × 10^–3 eV for the³He dµ ion and a resonance eigenvalue ofE=–58.225 303 eV and =0.118 × 10^–3 eV for the⁴He dµ ion have been obtained. These results are in a good agreement with the ones previously obtained by Kino and Kamimura by scattering calculation with the non-adiabatic coupled-rearrangement-channel method.     

D=2 and D=4 realization of κ-conformal algebra

We describe the generators of-conformal transformations leaving invariant the-deformed d'Alembert equation. For the case D=4 the algebraic structure of the conformal extension of the off-shell spin zero realization of-Poincaré algebra is discussed. Then the D=2 off-shell realization of-conformal algebra for arbitrary spin and its commutation relations are studied.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.Supported by KBN grant 2P 302 087 06.     

Effect of Laser Radiation near 1.5 µm on the Photoluminescence Parameters and the Ensemble of NV Centers in Diamond

JETP Letters - The effect of laser radiation with a wavelength near 1.55 µm on the photoluminescence properties of “nitrogen-vacancy” (NV) color centers in diamond has been studied...     

Design issues of 1.55 µm emitting GaInNAs quantum dots

We present a theoretical study of the optical properties of GaInNAs quantum dot (QD) structures, emitting at 1.55 µm wavelength. The theoretical model is based on a 10 × 10 k · p band-anti-crossing Hamiltonian, incorporating valence, conduction and nitrogen-induced bands. We have investigated the influence of the nitrogen to the conduction band mixing, and piezoelectric field on the ground state optical matrix element. For QDs grown on GaAs substrate with a reduced amount of indium and an increased amount of nitrogen in the QD the e _x polarized optical matrix element becomes on the average larger and less sensitive to the variation of both the QD shape and size than is the case of an InNAs QD. For the QD grown on InP substrate the dominant optical dipole matrix element is of the e _z light polarization. Our results identify the specific In and N content in the QDs required for optimal long-wavelength emission on both substrates.     

New effects in low energy scattering of pµ atoms

Strong solid state effects in low energy scattering of pμ atoms in solid hydrogen are reported and analyzed. Such effects have been observed in TRIUMF experiment E742 where muons are stopped in thin frozen (3 K) layers of hydrogen. Emission of low energy pμ atoms from the hydrogen layer into adjacent vacuum was much higher than expected, based on calculations which ignored the solid nature of hydrogen. Monte Carlo simulations, performed using the scattering cross-sections with solid state effects taken into account, show the important role of the coherent elastic Bragg scattering in the diffusion of pμ atoms. For pμ energies lower than the Bragg cut-off limit (∼2 meV) the total scattering cross-section falls by several orders of magnitude, the hydrogen target becomes transparent and the emission of cold pμ atoms takes place. This revised version was published online in August 2006 with corrections to the Cover Date.     

Jordanian twist quantization of D=4 Lorentz and Poincaré algebras and D=3 contraction limit

We describe in detail the two-parameter nonstandard quantum deformation of the D=4 Lorentz algebra , linked with a Jordanian deformation of . Using the twist quantization technique we obtain the explicit formulae for the deformed co-products and antipodes. Further extending the considered deformation to the D=4 Poincaré algebra we obtain a new Hopf-algebraic deformation of four-dimensional relativistic symmetries with a dimensionless deformation parameter. Finally, we interpret as the D=3 de Sitter algebra and calculate the contraction limit (R is the de Sitter radius) providing an explicit Hopf algebra structure for the quantum deformation of the D=3 Poincaré algebra (with mass-like deformation parameters), which is the two-parameter light-cone κ-deformation of the D=3 Poincaré symmetry.     

Development and Application of the 2D Relativistic Fokker-Planck Package

The Fokker Planck package which without the relativity effect has been developed in 2002. The package with relativity effect, which induced from Italy, is now developed. It conrains relativity effect, and is bounce averaged. It can deal with such as the trapping effect, wave heating, neutral beam injecting, and particle losses. It is very useful for our HL-2A experimental results analysis.     

Short-term frequency characteristics of 2 µm single frequency Solid-state lasers

The Short term frequency stability characteristics of 2 μm single frequency Solid-state lasers was investigated. The two laser systems of 2 μm single longitudinal mode oscillation Tm, Ho:YLF microchip laser and Ho:YAG NPRO laser were designed and constructed. The Short term frequency stability of these two laser were measured with the fiber delay self-beating heterodyne method. The 3dB width of the relative frequency fluctuation of Tm, Ho:YLF microchip laser and Ho:YAG NPRO laser were measured to be 895 and 736 Hz with 500 m fiber optical (2.5 μs delay). The proportional relation between the lasing fluctuation and the delay time were 358 and 263 Hz/μs, respectively. The vibration experiment was presented and it indicated that the NPRO Ho:YAG was more terrible to the influence of vibration, which is important in the practical application of wind measurement lidar.     

Measurement of various decay modes of charmed particlesD 0,D +,D s + andΛ s c

In the CERN NA 32 experiment a high-resolution silicon vertex detector and a purely topological approach have been used to investigate various decays of charmed particles. We observe ～620 fully reconstructed decays ofD ⁰ in 12 channels and determine the branching ratios. For fourD ⁰ decay modes involving a single (unseen) π⁰ the small and narrowD ^*+?D ⁰ mass difference is used to measure their branching ratios. We also observe ～280 fully reconstructedD ⁺ decays in 10 channels, ～90D _s ⁺ decays in 11 channels as well as 160Λ _s ^c and 18 decay channels ofD ⁺. For theD _s ⁺ , we measure the branching fractions within a subset of 16 three- and five-prong decay channels. For theΛ _s ^c , we determine the branching fractions within a sample of 11 three- and five-prong decay channels, nearly all involving a proton.     

The Effect of Active Region Heating on Dynamic and Power Characteristics of Quantum Cascade Lasers Emitting at a Wavelength of 4.8 µm at Room Temperature

Optics and Spectroscopy - Results of studying stripe quantum cascade lasers emitting at room temperature in the spectral range of 4.8 µm are presented. Power characteristics and turn-on...     

New approach to the old problem of muon sticking in µCF

A new approach is presented for evaluation of the muon sticking probability to helium in muon-catalyzed fusion reactions. Use of the sudden approximation is avoided. The probability _s of muon sticking to helium in the reaction dtµ µ⁴He+n, calculated with the new method, agrees with previous results. Moreover, the energy and angular distributions for the emitted muon, as well as the dependence of w_s on the energy radiated during the muon-catalyzed fusion event, have been evaluated.     

Magneto-optical trapping of bosonic and fermionic neon isotopes and their mixtures: isotope shift of the 3P2 ↔ 3D3 transition and hyperfine constants of the 3D3 state of 21Ne

We have magneto-optically trapped all three stable neon isotopes, including the rare ²¹Ne, and all two-isotope combinations. The atoms are prepared in the metastable ³P₂ state and manipulated via laser interaction on the ³P₂ ? ³D₃ transition at 640.2?nm. These cold (T ≈ 1?mK) and environmentally decoupled atom samples present ideal objects for precision measurements and the investigation of interactions between cold and ultracold metastable atoms. In this work, we present accurate measurements of the isotope shift of the ³P₂ ? ³D₃ transition and the hyperfine interaction constants of the ³D₃ state of ²¹Ne. The determined isotope shifts are (1625.9 ± 0.15)?MHz for ²⁰Ne ? ²²Ne, (855.7 ± 1.0)?MHz for ²⁰Ne ? ²¹Ne, and (770.3 ± 1.0)?MHz for ²¹Ne ? ²²Ne. The obtained magnetic dipole and electric quadrupole hyperfine interaction constants are A(³D₃) = (?142.4 ± 0.2)?MHz and B(³D₃) = (?107.7 ± 1.1)?MHz, respectively. All measurements give a reduction of uncertainty by about one order of magnitude over previous measurements.     

Comparison of ITG and TEM Microturbulence in DⅢ-D Tokamak

Microturbulence excited by ion temperature gradient(ITG)-dominant and trapped electron mode(TEM)-dominant instabilities is compared in the fusion plasmas using gyrokinetic simulations based on the realistic equilibrium data from DⅢ-D discharges.Collisions make a difference between two plasmas and give rise to similar results to those found in previous research experiments[Chin.Phys.Lett.35(2018)105201].The mode structures and frequency spectrum of the most unstable modes characterized by the ITG-dominant and TEM-dominant instabilities are excited in the lower and higher T. plasmas in the linear simulations.In the nonlinear simulations,contour plots of the perturbed potential are shown in the saturated stage,with the radial correlation lengths being microscopic on the order of the ion thermal gyroradius ρi in both the ITG and the TEM microturbulences.The dominant mode wavelengths of the perturbed potential increase when evolving from linear to nonlinear stages in both simulations, with the fluctuation energy spreading from the linearly dominant modes to the nonlinearly dominant modes.The radial correlation lengths are about 4ρi and the electron density fluctuation intensities are about 0.85% in the nonlinear saturated stage,which are in agreement with the experimental results.     

Implications of unitarity and analyticity for the Dπ form factors

We consider the vector and scalar form factors of the charm-changing current responsible for the semileptonic decay D → πlν. Using as input dispersion relations and unitarity for the moments of suitable heavy-light correlators evaluated with Operator Product Expansions, including O(α _s ²) terms in perturbative QCD, we constrain the shape parameters of the form factors and find exclusion regions for zeros on the real axis and in the complex plane. For the scalar form factor, a low-energy theorem and phase information on the unitarity cut are also implemented to further constrain the shape parameters. We finally propose new analytic expressions for the Dπ form factors, derive constraints on the relevant coefficients from unitarity and analyticity, and briefly discuss the usefulness of the new parametrizations for describing semileptonic data.