Infrared structure of non-abelian gauge theories: An instructive calculation

As a step towards an understanding of the infrared structure of non-Abelian gauge theories, we have calculated the anomalous magnetic moment of a colored quark up to fourth-order in the quark-gluon coupling constant g. The fourth-order result is infrared divergent. The infrared divergence is governed by the one loop contribution to the function β_λ(g) = λ dg/dλ, where λ is a small gluon-mass regulator. A differential equation which describes the infrared structure of the electromagnetic quark-form factors is proposed.     

Three-dimensional gravity-capillary waves on water — Small surface tension case

This paper considers three-dimensional gravity-capillary waves on water of finite-depth, which are uniformly translating in a horizontal propagating direction and periodic in a transverse direction. The exact Euler equations are formulated as a spatial dynamic system in which the variable used for the propagating direction is a time-like variable. The existence of the solutions of the system is determined by two non-dimensional constants, the Bond number b and the Froude number F, which in turn give the number of eigenvalues on the imaginary axis of the complex plane for the corresponding linearized operator around a uniform flow. Assume that λ=F⁻², C₁ is the curve in the (b,λ)-plane on which the first two eigenvalues for three-dimensional waves collide at the imaginary axis, and the intersection point of C₁ with {λ=1} is b₁>0. In this paper, the case for 0<b<b₁ and (b,λ) near C₁ is considered. A center-manifold reduction technique and a normal form analysis are applied to show that the dynamical system can be reduced to a system of ordinary differential equations. Using the existence of a homoclinic orbit connecting to a two-dimensional periodic (called generalized solitary-wave, thereafter) solution for the reduced system, it is shown that such a generalized solitary-wave solution persists for the original system by applying a perturbation method and adjusting some appropriate constants.     

Threshold conditions and bound states for locally periodic delta potentials

We present a systematic study of the conditions for the generation of threshold energy eigen states and also the energy spectrum generated by two types of locally periodic delta potentials each having the same strength λV and separation distance parameter a: (a) sum of N attractive potentials and (b) sum of pairs of attractive and repulsive potentials. Using the dimensionless parameter g = λV a in case (a) the values of g = g _n , n = 1, 2, …, N at which threshold energy bound state gets generated are shown to be the roots of Nth order polynomial D ₁(N, g) in g. We present an algebraic recursive procedure to evaluate the polynomial D ₁(N, g) for any given N. This method obviates the need for the tedious mathematical analysis described in our earlier work to generate D ₁(N, g). A similar study is presented for case (b). Using the properties of D ₁(N, g) we establish that in case (a) the critical minimum value of g which guarantees the generation of the maximum possible number of bound states is g = 4. The corresponding result for case (b) is g = 2. A typical set of numerical results showing the pattern of variation of g _n as a function of n and several interesting features of the energy spectrum for different values of g and N are also described.     

Berechnung des Magnetisierungs-„Ripple“ in ferromagnetischen dünnen Schichten

By means of straight forward analysis a complete calculation is given of magnetization ripple in polycrystalline ferromagnetic films. Wavelenghts and practical relations for ripple amplitude, length of coherence, and angle fluctuation are derived (which were so far only rather incompletely available from a very rough model of the ripple, given previously by the author). The dependence of ripple wavelength (λ ₀) on average crystallite sizea reaches a plateau at a definite critical valuea=a _g ∶λ ₀≈4a fora<a _g ,λ ₀ independent ofa fora>a _g , as has been found most recently byBaltz andDoyle.     

Quantum statistical theory of adsorption and desorption of a gas at a solid surface

The non-equilibrium initial value problem of phonon-mediated adsorption and desorption of a gas at a solid surface is formulated explicitly in a quantum-statistical theory and adsorption, flash desorption and isothermal desorption times are calculated using a non-local separable surface potential. We find that the flash desorption time is a function of both initial and final temperatures T_g and T_s and can, for fixed T_g, be approximated by Frenkel's formula over a limited range of flash temperatures T_s. We fit our theory to flash desorption data for He desorbing from Constantan and find excellent agreement. Predictions are given for the H/NaCl system. Isothermal and flash desorption times are correlated, and experiments are suggested to demonstrate the differences.     

Paramagnetic resonance of V in tetragonal GeO2

Anisotropic g and A tensors are found for V⁴⁺ in single crystal tetragonal GeO₂. The orbital mixing parameter λ, normalized radial average 〈1/r³〉/N and core polarization x/N are calculated, and λ is not anomalously low as reported from polycrystalline measurements.     

Measurement of the ortho-para transition rate in the pμp molecule and deduction of the pseudoscalar coupling constant gpμ

The ortho-para transition rate in the pμp molecule has been found experimentally to be λ_OP = (4.1 ± 1.4) × 10⁴ s^?1. Our recent result for the muon capture rate in liquid hydrogen can now be interpreted to extract the ortho-molecular capture rate: λ_OM = (531 ± 33) s^?1. A deduction of the pseudoscalar coupling constant g_p^μ is presented: we find g_p^μ = 8.7 ± 1.9.     

Gauge boson/Higgs boson unification: The Higgs bosons as superpartners of massive gauge bosons

The N = 4 supergravity theories with local SO(4) invariance are formulated in superspace. The gauged SO(4) theory with two coupling constants (g₁, g₂) is shown to reduce to three inequivalent models: g₁ = g₂ with negative cosmological constant, g₁ = ?g₂ with positive cosmological constant, and g₁ = 0, g₂ ≠ 0 which is a particular case of the Freedman-Schwarz gauged SU(2) ? SU(2) model. The Higgs effect in the vector-scalar sector of the gauged N = 5 supergravity is analyzed.     

QCD asymmetry and polarized hadron structure function measurement

It is shown that in hard processes with a single polarized particle contributions proportional to two-arguments distribution functions (parton correlation densities) can receive imaginary parts even from the Born subprocess. This results in large (not proportional to α_s) single asymmetries. Such an asymmetry is calculated in the process λN↑ → λX, which can serve as a good parton meter for the correlation densities.     

Asymptotics of Self-similar Solutions to Coagulation Equations with Product Kernel

We consider mass-conserving self-similar solutions for Smoluchowski’s coagulation equation with kernel K(ξ,η)=(ξη) ^λ with λ∈(0,1/2). It is known that such self-similar solutions g(x) satisfy that x ^?1+2λ g(x) is bounded above and below as x→0. In this paper we describe in detail via formal asymptotics the qualitative behavior of a suitably rescaled function h(x)=h _λ x ^?1+2λ g(x) in the limit λ→0. It turns out that \(h \sim 1+ C x^{\lambda/2} \cos(\sqrt{\lambda} \log x)\) as x→0. As x becomes larger h develops peaks of height 1/λ that are separated by large regions where h is small. Finally, h converges to zero exponentially fast as x→∞. Our analysis is based on different approximations of a nonlocal operator, that reduces the original equation in certain regimes to a system of ODE.     

Saturated absorption spectroscopy: Elimination of crossover resonances with the use of a nanocell

It is demonstrated that the velocity-selective optical pumping/saturation resonances of the reduced absorption in a Rb vapor nanocell with thickness L = λ, 2λ, and 3λ (resonant wavelength λ = 780 nm) allow for the complete elimination of crossover (CO) resonances. We observe well-pronounced resonances corresponding to the F _g = 3 → F _e = 2, 3, and 4 hyperfine transitions of the ⁸⁵Rb D₂ line with line widths close to the natural width. A small CO resonance located midway between F _g = 3 → F _e = 3 and F _g = 3 → F _e = 4 transitions appears only for L ≥ 4λ. The D₂ line (λ = 852 nm) in a Cs nanocell exhibits a similar behavior. From the amplitude ratio of the CO and VSOP resonances, it is possible to determine the thickness of the column of alkali vapor in the range of 1–1000 μm. The absence of the CO resonances for nanocells with L ～ λ is attractive for the frequency reference application and for studying the transitions between the Zeeman sublevels in external magnetic fields.     

Effects of cross-correlation between the real and imaginary parts of the quantum noise in a two-mode saturation laser system

A two-mode saturation laser model with cross-correlation between the real and imaginary parts of the quantum noise is considered. The laser intensity Langevin equation and corresponding Fokker-Planck equation are derived by the phase-locking method. The effects of the cross-correlation strength λ between the real and imaginary parts of quantum noise and the cavity decay constant K on the steady-state intensity distribution Q(I₁,I₂), the mean light intensity 〈I〉, the normalization autocorrelation λ₁₁(0) and cross correlation λ₁₂(0) are studied by numerical calculation. The results show that as λ increases the Qs(I₁,I₂) show two extrema, and λ almost does not affect the 〈I〉, λ₁₁(0) and λ₁₂(0) when the laser system is operated far above threshold. Nevertheless, when the laser system is operated at and below threshold, λ makes the curves of Qs(I₁,I₂) have the higher peak and drop faster. Furthermore, it enhances the deviation of λ₁₁(0) and λ₁₂(0) and lessens the mean light intensity 〈I〉 when the laser system is operated at and below threshold.     

On the existence of interacting perturbatively nonrenormalizable quantum field theories

We study the effective potential of three perturbatively nonrenormalizable scalar field theories, (λ φ ⁴+g φ ⁶)₃₊,λ φ ₄₊₁ ⁴ andλ φ ₅₊₁ ⁴ , by nonperturbative methods. The requirements of existence, finiteness and interaction seem to demand such a weak nonrenormalizable interaction that no or little effects remain at the quantum level.     

E.S.R. evidence for the planarity of the t-butyl radical

Monte Carlo calculations are reported for the radial distribution function g ₂(r; λ) of a fluid in which the intermolecular pair potential is [u ^ref(r) + λu ^p(r)], u ^ref(r) being the Weeks-Chandler-Andersen (WCA) reference fluid, and [u ^ref(r) + u ^p(r)] being the Lennard-Jones (6, 12) fluid. The calculations are performed for λ values in the range 0 to 1, at the state condition ρσ³ = 0·80, kT/ε = 0·719. It is shown that at high densities the perturbation expansion of g ₂(r; λ = 1) about g ₂(r; λ = 0) is rapidly convergent, but that the corresponding expansion for y ₂(r; λ) = exp [βu(r; λ)] × g ₂(r; λ) is not. In addition Monte Carlo estimates of the individual terms that contribute to the first-order perturbation term, (?g ₂/?λ)_λ=0, are presented. It is shown that these terms are individually large, but that (?g ₂/?λ)_λ=0 is small because there is strong cancellation between the various terms. Consequently, the calculation of (?g ₂/?λ)_λ=0 is highly sensitive to the approximation used to evaluate the individual terms.     

Spectroscopic studies of tantalum doped borate glasses

Glasses with formula 30Li₂O 60B₂O₃xTa₂O₅ (10−x) Bi₂O₃ for x=0, 2, 4, 6 and 8 were prepared via normal melt quenching technique and characterized by refractive index and MDSC. Refractive index (μ) and glass transition temperature (T_g) are found to increase with increase in dopant concentration. Impedance spectra of the samples were recorded in the frequency range 100 Hz–5 MHz in the temperature range 175–275 °C. The plots are typical of those recorded for disordered systems. Conductivities and relaxation times are found to follow Arrhenius type of relation and activation energies are calculated. Optical absorption spectra were recorded in the wavelength range 200–900 nm range from which cutoff wavelength (λ_c) and optical band gap energy (E_g) are evaluated. λ_c is found to decrease while E_g to increase with increase in composition. FTIR spectra of the samples were recorded in the frequency range 400–1500 cm⁻¹ which exhibit characteristic bands corresponding to BO₃, BO₄ stretching vibrations and BO bending vibration. Tightening of the structure is indicated by increase in the vibration of BO₃ at the cost of BO₄ for 8 mol% of Ta₂O₅. This is in support of the highest value of T_g for this sample among the series. Raman spectra of the samples were recorded in the frequency range 200–1200 cm⁻¹. With successive addition of Ta₂O₅, increase in the vibration of Ta–O groups TaO₆ groups to be responsible for observed increase in μ and T_g. An attempt is made to prepare tantalum doped borate glasses and study them by spectroscopic techniques.     

Search for macroscopic CP violating forces using a neutron EDM spectrometer

The search for CP violating forces between nucleons in the so-called axion window of force ranges λ between 2 × 10^?5 m and 0.02 m is interesting because only little experimental information is available there. Axionlike particles would induce a pseudo-magnetic field for neutrons close to bulk matter. A laboratory search investigates neutron spin precession close to a heavy mirror using ultracold neutrons in a magnetic resonance spectrometer. From the absence of a shift of the magnetic resonance we established new constraints on the coupling strength of axion-like particles in terms of the product g _s g _p of scalar and pseudo-scalar dimensionless constants, as a function of the force range λ, g _s g _p λ² ≤ 2 × 10^?21 [cm²] (C.L.95%) for 10^?4 cm < λ < 1 cm. For 0.1 cm < λ < 1 cm previous limits are improved by 4 to 5 orders of magnitude.     

The millimeter wavelength spectrum of diatomic sulfur

The gas phase spectrum of diatomic sulfur has been detected in the millimeter wave-length region. Six lines have been measured. The rotational and fine structure parameters obtained are B₀ = 8831.8676 ± 0.006 MHz, D₀ = 5.9 ± 0.7 kHz, λ₀ = 353040 ± 27 MHz, and γ₀ = ? 200.9 ± 0.7 MHz. In addition, reanalysis of EPR data has yielded g_z + 1.18g_n = 2.0021 + 0.0014 and g_z - g_⊥ = ?0.0089 ± 0.0017. On the basis of the frequencies obtained in this work, it was also possible to exclude the assignment of several interstellar emissions to the sulfur dimer.     

Design and analysis of slow light regime in silicon carbide 2D photonic crystal waveguides

We theoretically demonstrate the slow light capabilities of 2D silicon carbide based photonic crystal W1 waveguides (SiC-PhC-W1Ws) with numerical simulations. The PhC is assumed to be created by devising air-holes with hexagonal lattice in a standard SiC substrate having oscillator type ordinary refractive index. Numerical simulations show that by means of selective optofluidic infiltration and varying the air-holes radii, SiC-PhC-W1Ws are capable of slowing light down by about 473 times while their group velocity dispersions are tailored to near zero values. Our numerical study also suggests the possibility of slow-light guiding with n_g × Δλ/λ_c values as high as 0.42 in SiC-PhC-W1Ws at optical telecommunications wavelengths.