Primordial <Superscript>4</Superscript>He Abundance Constrains the Possible Time Variation of the Higgs Vacuum Expectation Value

We constrain the possible time variation of the Higgs vacuum expectation value (v) by recent results on the primordial ⁴He abundance (Y _P ). For that, we use an analytic approach which enables us to take important issues into consideration, that have been ignored by previous works, like the v-dependence of the relevant cross sections of deuterium production and photodisintegration, including the full Klein–Nishina cross section. Furthermore, we take a non-equilibrium Ansatz for the freeze-out concentration of neutrons and protons and incorporate the latest results on the neutron decay. Finally, we approximate the key-parameters of the primordial ⁴He production (the mean lifetime of the free neutron and the binding energy of the deuteron) by terms of (where v ₀ denotes the present theoretical estimate). Eventually, we derive the relation and the most stringent limit on a possible time variation of v is given by: .     

Density functional study of structural and electronic properties of Al<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>P (2 ≤ <Emphasis Type="Italic">n</Emphasis> ≤ 12) clusters

Low-lying equilibrium geometric structures of Phosphorus-doped aluminum cluster Al _n P (n = 2–12) clusters obtained by an all-electron linear combination of atomic orbital approach, within spin-polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three-parameter hybrid generalized gradient approximation (GGA) due to Becke-Lee-Yang-Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static polarizabilities are calculated for the ground-state structures within the GGA. It is observed that symmetric structures with the P atom occupying a peripheral position are lowest-energy geometries of Al _n P (n = 2, 4–11), while the P impurities of Al₃P and Al₁₂P prefer to occupy internal sites in the aluminum clusters. Generalized gradient approximation extends bond lengths as compared to the LSDA lengths. The odd-even oscillations in the dissociation energy, the second differences in energy, the HOMO–LUMO gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within both GGA and LSDA. The stability analysis based on the energies clearly shows the clusters with an even number of valence electrons are more stable than clusters with odd number of valence electrons.     

Homotopy Approach to Quantum Gravity

Gravity may be a quantum-space-time effect. General relativity is quantized by small generic changes in its commutation relations that make its Lie algebras simple on all levels, positing extra variables frozen by self-organization as needed. This quantizes space-time coordinates as well as fields and eliminates physical singularities. Fermi statistics and sl (nℝ) Lie algebras are assumed for all levels. Spin 1/2 is taken to be anomalous, arising from vacuum organization; the spin-statistics relation is incorporated. The gravitational field is quartic in Fermi variables. Einstein’s non-commutativity of parallel transport emerges as a vestige of Heisenberg’s quantum non-commutativity near the classical limit.     

Brownian Approximation and Monte Carlo Simulation of the Non-Cutoff Kac Equation

The non-cutoff Boltzmann equation can be simulated using the DSMC method, by a truncation of the collision term. However, even for computing stationary solutions this may be very time consuming, in particular in situations far from equilibrium. By adding an appropriate diffusion, to the DSMC-method, the rate of convergence when the truncation is removed, may be greatly improved. We illustrate the technique on a toy model, the Kac equation, as well as on the full Boltzmann equation in a special case.     

Quantum Stochastic Convolution Cocycles II

Schürmann’s theory of quantum Lévy processes, and more generally the theory of quantum stochastic convolution cocycles, is extended to the topological context of compact quantum groups and operator space coalgebras. Quantum stochastic convolution cocycles on a C*-hyperbialgebra, which are Markov-regular, completely positive and contractive, are shown to satisfy coalgebraic quantum stochastic differential equations with completely bounded coefficients, and the structure of their stochastic generators is obtained. Automatic complete boundedness of a class of derivations is established, leading to a characterisation of the stochastic generators of *-homomorphic convolution cocycles on a C*-bialgebra. Two tentative definitions of quantum Lévy process on a compact quantum group are given and, with respect to both of these, it is shown that an equivalent process on Fock space may be reconstructed from the generator of the quantum Lévy process. In the examples presented, connection to the algebraic theory is emphasised by a focus on full compact quantum groups.     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.     

LD-end-pumped Nd:YAP laser operating at 1341.4 nm and doubling of its frequency

We report an LD-end-pumped linearly-polarized continuous-wave (CW) Nd:YAP laser operating at 1341.4 nm. Making use of the plane-concave resonator (T = 2.4%) and the plane-plane resonator (T = 2.6%), we obtain linearly-polarized laser radiation at 1341.4 nm with a power of 3.15 and 2.86 W and corresponding optical slope efficiency of 18.4 and 17.5%, respectively. The effect of the laser oscillation mode on the output is analyzed. An experiment on the intra-cavity frequency doubling with an LBO crystal has been performed, and a laser power of 431 mW in one direction at 670.7 nm was obtained.     

First-principles studies of the electronic structure and optical properties of AgBO<Subscript>3</Subscript> (B=Nb,Ta) in the paraelectric phase

The electronic energy-band structure, density of states (DOS), and optical properties of AgBO₃ in the paraelectric cubic phase have been studied by using density functional theory within the local density approximation for exchange-correlation for the first time. The band structure shows a band gap of 1.533 eV (AgNbO₃)and 1.537 eV (AgTaO₃)at (M-⌈)point in the Brillouin zone. The optical spectra of AgBO₃ in the photon energy range up to 30 eV are investigated under the scissor approximation. The real and imaginary parts of the dielectric function and — thus the optical constants such as reflectivity, absorption coefficient, electron energy-loss function, refractive index, and extinction coefficient — are calculated. We have also made some comparisons with related experimental and theoretical data that is available.      

Linear polarization Yb<Superscript>3+</Superscript>-doped fiber laser with novel innerclad structures

Results on high radiance Yb³⁺-doped fiber lasers with novel double innerclad structures (double-D clad and four hole) and polarized output at ≈1090 nm are presented. We have demonstrated >40% of the total output power being polarized, making the fiber laser suitable for LIDAR and second-harmonic generation (SHG) applications. It also showed a 10-nm tuning range with low (less than 10 mW) average power variations. The narrow linewidth source was pumped with a low cost, low brightness laser diode, and exhibited a relatively low slope efficiency, which gives room for improvement by using a 976-nm pump source where Yb³⁺ has a narrower linewidth and at least five times higher absorption.