Lowest-order Contribution Research Articles

Dynamical evolution of Rayleigh-Taylor and Richtmyer-Meshkov mixing fronts.

Dynamic behavior of mixing fronts plays a crucial role in multifluid turbulent mixing. In this paper, we derive an analytic solution for the dynamic evolution of mixing fronts driven by constant acceleration Rayleigh-Taylor (RT) and impulsive acceleration Richtmyer-Meshkov instabilities, from a simple physics model expressed as a pair of ordinary differential equations. An approximate closed form asymptotic evaluation of the RT solution is obtained, through terms of order O(1), as t--> infinity. This three term expansion, including lower order terms, is used to interpret experimental and simulation data. Our solutions improve on previous analyses in their agreement with experimental data, in that we can fit both the slope and the intercept of the Z(b) vs Agt(2) experimental plots by adjusting parameters in our model. Since the experimental data are close to self-similar, the improvement due to the lower order contributions in the asymptotic expansion is modest. We also apply this analysis to simulation data, for which preasymptotic data exist. We reexamine previous simulation data and determine an improved growth rate alpha(b)=0.0625. The present paper provides concepts and tools to explore the preasymptotic aspects of these data.

Chiral anomaly and high-energy scattering in QCD

Infra-red properties of the triangle anomaly and the ``anomaly pole'' are elaborated and applied to the study of high-energy scattering in QCD, when the gauge symmetry is partially broken to SU(2). It is shown that the chiral flavor anomaly provides a wee-gluon component for Goldstone bosons that combines with interactions due to the U(1) anomaly to produce an infra-red transverse momentum scaling divergence in scattering amplitudes. After the divergence is factorized out, as a wee-gluon condensate in the infinite momentum pion, the remaining physical amplitudes have confinement and chiral symmetry breaking. A lowest-order contribution to the pion scattering amplitude is calculated in detail. Although originating from very complicated diagrams, the amplitude has a remarkable (semi-)perturbative simplicity. The momentum structure is that of single gluon exchange but zero momentum quarks inject additional spin and color structure via anomaly interactions.

Letter: Antisymmetric Tensor Contribution to the Muon g - 2

We investigate the Kalb-Ramond antisymmetric tensor field as solution to the muon $g-2$ problem. In particular we calculate the lowest-order Kalb-Ramond contribution to the muon anomalous magnetic moment and find that we can fit the new experimental value for the anomaly by adjusting the coupling without affecting the electron anomalous magnetic moment results.

The magnetic moments of the octet baryons in quenched chiral perturbation theory

We compute the magnetic moments of the octet baryons up to two orders in quenched chiral perturbation theory. In addition to the ∼ m q contributions that arise in QCD, there are lower-order contributions of the form M 0 2log m q from loop diagrams involving hairpin interactions.

Ionization potential of the helium atom.

The ground-state ionization potential of the He4 atom is found to be 5 945 204 223 (42) MHz. Along with lower-order contributions, this result includes all effects of relative order alpha4, alpha(3)m(e)/m(alpha), and alpha(5)ln(2)alpha. Effective operators derived in dimensionally regularized nonrelativistic quantum electrodynamics are employed. The average values of these operators are evaluated using a high-accuracy variational wave function constructed in an exponential basis.

Fermion helicity flip by parity violating torsion

The helicity flip of a spin-1/2 Dirac fermion interacting with a torsion- field endowed with a pseudo-tensorial extension is analysed. Taking the torsion to be represented by a Kalb-Ramond field, we show that there is a finite amplitude for helicity flip for massive fermions. The lowest order contribution is proportional to the pseudo-tensor term.

IMPLICIT DENSITY FUNCTIONALS FOR THE EXCHANGE-CORRELATION ENERGY: DESCRIPTION OF VAN DER WAALS BONDS

The energy surface of the Helium dimer, as a prototype of a van der Waals bond molecule, is investigated within the framework of density functional theory. For the exchange-correlation energy an implicit density functional, depending on the Kohn-Sham orbitals, is applied in which exchange is treated exactly, while correlation is approximated by the lowest order contribution obtained by Kohn-Sham perturbation theory. The resulting energy surface is in fair quantitative agreement with highly accurate empirical data over the complete range of internuclear separations, demonstrating that the concept of orbital-dependent functionals can provide a seamless description of dispersion forces. As selfconsistent calculations with implicit functionals on the basis of the optimized potential method are rather time-consuming, the correlation part of the exchange-correlation functional is evaluated perturbatively in the Helium dimer calculations. However , we also present an approximate scheme for the evaluation of the corresponding correlation potential.

On the validity region of Fermi-liquid description of 3D strongly correlated systems

The decay of quasiparticles in systems with strongly correlated electrons (SSCE) is investigated. The difference with normal Fermi-liquid (FL) behavior is caused by kinematic interactions. The latter originate (in SSCE) from hopping and mixing interaction which in normal FL just modify bands, but do not cause a decay. Using a diagram technique we derive the lowest-order contribution giving decay and show how it varies with filling and with the position of the Fermi level with respect to the upper Hubbard's sub-band. Examples are given for a simple-cubic 3D-lattice. Due to spin dependence of the vertex functions a big effect on the lifetime of the quasi-particles due to magnetic fields is expected. A possible experimental realization is discussed.

Conductivity of disordered electrons: Mean-field approximation containing vertex corrections

The electrical {\em dc}-conductivity of disordered, non-interacting electrons is calculated in the asymptotic limit of high lattice dimensions $d\to \infty$. To go beyond the lowest-order contribution in the expansion parameter $1/d$ of the single bubble diagram, vertex corrections are calculated from an asymptotic expression for the two-particle vertex. A mean-field approximation for the dc-conductivity containing the leading high-dimensional vertex corrections is proposed which is free of spurious non-analyticities, i.e. the conductivity is non-negative and shows no unphysical behavior in $d\geq 3$.

Angular distribution of light scattered from a sinusoidal grating

The angular distributions of light scattered by gold-coated and aluminum-coated gratings with amplitudes of approximately 90 nm and periods of 6.67 microm were measured and calculated for light incident from a He-Ne laser at an angle of 6 degrees. Experimental results are compared with predictions of Beckmann's scalar theory and Rayleigh's vector theory. The measured scattering pattern has a background of scattered light due mainly to residual surface roughness. Also the power in the higher-order peaks is larger by several orders of magnitude than the computed one, which can be attributed mainly to the low-order contributions of the harmonics in the profile.

Trapping in AC octode field cages

Three-dimensional micro-electrode systems, fabricated by IC technology, were used for the trapping and aggregation of suspended microscopic dielectric particles. To achieve negative dielectrophoresis (repelling forces) in aqueous solution, phase-shifted RF electric fields were applied to the micro-electrodes. Reliable dielectrophoretic trapping in a liquid stream usually requires dipole forces (lowest order contribution). Due to symmetry, AC (two-phase) field cages are not closed in dipole approximation. We introduce a new AC drive of octode cages that allows efficient trapping against streaming at much lower expense than rotating (four-phase) electrode excitation. This is confirmed analytically, numerically and by experiments using latex beads.

Theoretical description of the nonlinear response functions associated with eight distinctive three-dimensional vibrational spectroscopies

The three-dimensional (3D) vibrational spectroscopies are theoretically considered in terms of the associated nonlinear response functions. Since the 3D vibrational spectroscopy involves three vibrational coherence evolutions in the ground electronic state, it is found that there are eight distinctive possibilities when a vibrational coherence state can be created via an infrared field–matter interaction or two off-resonant optical field–matter interactions via Raman. The nonlinear response functions associated with eight distinctive 3D vibrational spectroscopies, where seven of them are novel methods, are presented and expressed in terms of the linear response functions by taking the lowest-order contributions. The analytic expressions of the 3D Fourier spectra are obtained. By using the results, how to utilize the 3D vibrational spectroscopic methods to measure the higher-order vibrational mode coupling arising from the anharmonicity of the multidimensional potential energy surface as well as from the nonlinearity of the dipole moment or polarizability with respect to the vibrational degrees of freedom is discussed. Numerical calculations of the results for a three-oscillator model system are presented, and a few characteristic peaks uniquely appearing in the 3D vibrational spectra are discussed in detail. Finally, the third-order nonlinear terms of dipole moment and polarizability are found to be of critical use in the structure determination, assuming that the collective dipole moment and polarizability is mainly determined by the dipole-induced–dipole interaction effect.

Rotating wave approximation: systematic expansion and application to coupled spin pairs

We propose a new treatment of the dynamics of a periodically time-dependent Liouvillian by mapping it onto a time-independent problem and give a systematic expansion for its effective Liouvillian. In the case of a two-level system, the lowest order contribution is equivalent to the well-known rotating wave approximation. We extend the formalism to a pair of coupled two-level systems. For this pair, we find two Rabi frequencies and we can give parameter regimes where the leading order of the expansion is suppressed and higher orders become important. These results might help to investigate the interaction of tunneling systems in mixed crystals by providing a tool for the analysis of echo experiments.

Analytical model of the “Shot Noise” effect in photoresist

Decreasing feature size implies increased sensitivity to statistical fluctuations in various process parameters such as dose and the number of relevant bonds broken during post exposure bake. Here we develop a generic analytical model which accounts for essentially all these effects. The lowest order contribution to surface roughness from the bond statistics alone are shown to be very similar to recent experimental data. The lowest order contribution to a scaling law for predicting edge roughness is also derived.

Nonrelativistic pion interactions and the pionium lifetime

We construct an effective Lagrangian for interacting pions with non-relativistic energies. The coupling constants can be expressed in terms of the different scattering lengths and slopes. When used in the calculation of the pionium decay rate, the scattering slope contribution gives a correction of about 8% compared with the lowest order contribution coming from the scattering lengths alone.

Vibrational and electronic second hyperpolarizabilities of all-trans polysilane chains

The vibrational (γLv) and electronic (γLe) longitudinal second hyperpolarizabilities of increasingly large polysilane chains are determined at the Hartree–Fock 6-31G level by adopting both the double harmonic oscillator approximation and the infinite optical frequency finite field relaxation procedure. The relative importance of the electronic, Raman, infrared/hyperRaman and lowest-order anharmonicity contributions to the second hyperpolarizability is evaluated for the most common nonlinear optical (NLO) processes. At the double harmonic oscillator level of approximation the most contributing vibrational normal modes to γLv are characterized as a function of the polysilane chain length. Comparisons with experimental and other theoretical studies are carried out in what concerns the infrared and Raman vibrational spectra as well as the NLO properties of various oligosilanes and polysilanes.

Non-linear evolution of the tidal angular momentum of protostructures — II. Non-Gaussian initial conditions

The formalism that describes the non-linear growth of the angular momentum L of protostructures from tidal torques in a Friedmann Universe, as developed in a previous paper, is extended to include non-Gaussian initial conditions. We restrict our analysis here to a particular class of non-Gaussian primordial distributions, namely multiplicative models. In such models, strongly correlated phases are produced by obtaining the gravitational potential via a nonlinear local transformation of an underlying Gaussian random field. The dynamical evolution of the system is followed by describing the trajectories of fluid particles using second-order Lagrangian perturbation theory. In the Einstein-de Sitter universe, the lowest-order perturbative correction to the variance of the linear angular momentum of collapsing structures grows as t^8/3 for generic non-Gaussian statistics, which contrasts with the t^10/3 growth rate characteristic of Gaussian statistics. This is a consequence of the fact that the lowest-order perturbative spin contribution in the non-Gaussian case arises from the third moment of the gravitational potential, which is identically zero for a Gaussian field. Evaluating these corrections at the maximum expansion time of the collapsing structure, we find that these non-Gaussian and non-linear terms can be as high as the linear estimate, without the degree of non-Gaussianity as quantified by skewness and kurtosis of the density field being unacceptably large. The results suggest that higher-order terms in the perturbative expansion may contribute significantly to galactic spin which contrasts with the straightforward Gaussian case.

Nonlinear acoustic and microwave absorption in glasses

A theory of weakly-nonlinear low-temperature relaxational absorption of acoustic and electromagnetic waves in dielectric and metallic glasses is developed. Basing upon the model of two-level tunneling systems we show that the nonlinear contribution to the absorption can be anomalously large. This is the case at low enough frequencies, where freqeuency times the minimal relaxation time for the two-level system are much less than one. In dielectric glasses, the lowest-order nonlinear contribution is proportional to the wave's intensity. It is negative and exhibits anomalous frequency and temperature dependencies. In metallic glasses, the nonlinear contribution is also negative, and it is proportional to the square root of the wave's intensity and to the frequency. Numerical estimates show that the predicted nonlinear contribution can be measured experimentally.

Triangle amplitude with off-shell Coulomb T matrix for exchange reactions in atomic and nuclear physics.

The lowest-order rescattering contribution (triangle amplitude) in three-body models of exchange reactions with charged particles contains the off-shell two-body T matrix describing the intermediate-state Coulomb scattering of charged subsystems. General properties of the exact exchange triangle amplitude, when the incoming and outgoing particles are on the energy shell, are derived. This includes the analytic behavior, i.e., the positions and characters of its leading singularities, in the cos\ensuremath{\vartheta} plane, where \ensuremath{\vartheta} is the scattering angle, in the vicinity of the forward- and backward-scattering directions. Since for computational reasons the Coulomb T matrix is usually replaced by the Coulomb potential, the effects of such an approximation on the analytic properties are investigated. The theoretically established behavior of the exact and the approximate exchange triangle amplitudes is then illustrated by numerical calculations, for both atomic and nuclear reactions, for energies below and above the corresponding three-body dissociation thresholds, for elastic and inelastic exchange. \textcopyright{} 1996 The American Physical Society.

Lowest-order contribution of soft gluon rescattering for large rapidity gap events in DIS

Using a powerful PQCD technique developed by Luo, Qiu and Sterman, we derive the diffractive structure functions at the lowest order. The procedure leading to these results is straightforward. More importantly, in this approach, we find that, effectively, there are no double hard scatterings of gluons responsible for the diffractive process at lowest order. The dominant scattering process must involve a soft gluon. This soft gluon contributes to the process only by adding two colour vertex terms to the cross section without affecting the kinematic state, thus the kinematics is the same as that of the PGF process. Our approach displays the important role played by the soft gluon in LRG events exactly.