Higher-order Couplings Research Articles

Analysis of the ε-Expansion in Turbulence Theory: Approximate Renormalization Group for Diffusion of a Passive Scalar in a Random Velocity Field

The validity of the e-expansion in the turbulence problem is discussed using the example of diffusion of a passive scalar in a random velocity field. A generalization of Wilson's rule for calculating a diagram of arbitrary order is introduced. The resulting perturbation series, while having zero radius of convergence, is summed exactly yielding amplitudes which differ from those obtained to lowest order in the e-expansion by only a few percent. The properties of the expansion are analyzed in detail and it is shown that various subsets of diagrams, while differing by an infinite number of terms, give close results in the vicinity of the fixed point. This indicates nontrivial compensation of high-order interactions in turbulence. The irrelevance of high-order couplings is demonstrated for arbitrary values of e. The quality the approximation is tested by comparison with numerical experiments on diffusion of a passive scalar in a band-limited random velocity field in the limit of infinite Peclet number.

On the importance of higher order anharmonic molecular couplings

The dynamics of molecular vibrational dephasing (IVR) are governed by the coupling structure of the vibrational Hamiltonian. We use a recently developed factorization model for normal coordinate potentials to compare the importance of direct high order couplings to both direct low order couplings and low-order coupling chains. The importance of high order couplings is characterized as a function of the vibrational energy and of molecular size. Particular attention is paid to phase cancellation effects in coupling chains, and to correlations between vibrational modes depending on their localization length. To account properly for IVR at high densities of states and long times, high order couplings must be taken into account.

Quantum tunneling in nuclear fusion

Recent theoretical advances in the study of heavy-ion fusion reactions below the Coulomb barrier are reviewed. Particular emphasis is given to new ways of analyzing data (such as studying barrier distributions), new approaches to channel coupling (such as the path-integral and Green's function formalisms), and alternative methods to describe nuclear structure effects (such as those using the interacting boson model). The roles of nucleon transfer, asymmetry effects, higher-order couplings, and shape phase transitions are elucidated. The current status of the fusion of unstable nuclei and very massive systems are briefly discussed.

Importance of nonlinear couplings in fusion-barrier distributions and mean angular momenta

The effects of higher-order coupling of surface vibrations to the relative motion on heavy-ion fusion reactions at near-barrier energies are investigated. The coupled-channels equations are solved to all orders, and also in the linear and the quadratic-coupling approximations. It is shown that the shape of fusion-barrier distributions and the energy dependence of the average angular momentum of the compound nucleus can significantly change when the higher-order couplings are included. The role of octupole vibrational excitation of in the fusion reaction is also discussed using the all-order coupled-channels equations.

The Water Vapor Linestrengths between 11 600 and 12 750 cm−1

The water vapor linestrengths in the region of the 3ν + δ resonance polyad of interacting vibrational states (the corresponding upper states are (310), (211), (112), (013), (131), (230), (032), and (051)) have been analyzed leading to accurate dipole moment transition parameters. The effective rotational Hamiltonian constants used to calculate the vibration–rotation wavefunctions (J.-M. Flaud, C. Camy-Peyret, A. Bykov, O. Naumenko, T. Petrova, A. Scherbakov, L. Sinitsa, 1994.J. Mol. Spectrosc.183,300–309) take into account both strong centrifugal distortion effects and dark states presence. These effects are known to be important for the highly excited vibrational states of water-like molecules. The input data set included the line intensities measured by Toth (R. Toth, 1994.J. Mol. Spectrosc.166,176–183) and the line intensities of the weak bands 2ν1+ 3ν2, 3ν2+ 2ν3, and 3ν1+ ν2derived from peak absorptions of a spectrum recorded at a pressure of 17.0 Torr and a path length of 434 m. The parameters of the effective dipole moment operator determined by least square fitting give a very satisfactory agreement with experimental values since the mean error for the 876 experimental linestrengths is only 3.9%. It is worth noticing that such an agreement could be reached only because high-order resonance couplings with dark states were explicitly taken into account.

Approximate factorization of molecular potential surfaces. I. Basic approach

The intermediate vibrational energy regime—well above the zero point, yet below the first dissociation limit—plays an important role in many molecular processes, such as radiationless transitions or intramolecular vibrational energy redistribution (IVR). For molecules with 𝒩>6 vibrational degrees of freedom, the calculation of energy levels and spectra of the full anharmonic vibrational Hamiltonian at high energies presents a formidable problem. Here we derive an asymptotic factorization of the potential energy surface (PES) based on the global topography of molecular potentials. The resulting approximate models require only a few input parameters such as vibrational frequencies and cubic anharmonicities. They are compared to benchmark PES derived from curvilinear model potentials and Monte Carlo sampled ab initio calculations for several small molecules. Higher order couplings are found to make a significant contribution to IVR decays at long times.

Higher-order gravitational couplings and modular forms in N = 2, D = 4 heterotic string compactifications

Higher-order gravitational couplings and modular forms in N = 2, D = 4 heterotic string compactifications

Coupled channels analysis of high precision fusion data.

High precision fusion data for $^{16}\mathrm{O}$${+}^{144}$Sm are analyzed in a coupled channels treatment which includes the excitation of the lowest ${2}^{+}$ and ${3}^{\mathrm{\ensuremath{-}}}$ states in both projectile and target. We find that certain higher-order couplings, which are often neglected in coupled channels analyses, play a significant role and improve the fit to the data. The nuclear potential which gives the best fit has a diffuseness of 0.64 fm. This is consistent with the prediction of folding models and also with the empirical expectation, based on analyses of elastic scattering data. \textcopyright{} 1996 The American Physical Society.

Higher-order gravitational couplings and modular forms in N = 2, D = 4 heterotic string compactifications

The restrictions of target-space duality are imposed at the perturbative level on the holomorphic Wilsonian couplings that encode certain higher-order gravitational interactions in N = 2, D = 4 heterotic string compactifications. A crucial role is played by non-holomorphic corrections. The requirement of symplectic covariance and an associated symplectic anomaly equation play an important role in determining their form. For models which also admit a type-11 description, this equation coincides with the holomorphic anomaly equation for type-II compactifications in the limit that a specific Kähler-class modulus grows large. We explicitly evaluate some of the higher-order couplings for a toroidal compactification with two moduli T and U, and we express them in terms of modular forms.

Nonlinear Damping of Oscillations in Tidal-Capture Binaries

We calculate the damping of quadrupole f- and low-order g-modes (primary modes) by nonlinear coupling to other modes of the star. Primary modes destabilize high-degree g-modes of half their frequency (daughter modes) by 3-mode coupling in radiative zones. For Sun-like stars, the growth time ≡η<SUP>-1</SUP>≍4E<SUP>-½</SUP><SUB>0,42</SUB> days, where E<SUB>0,42</SUB> is the initial energy of the primary mode in units of 10<SUP>42</SUP> ergs, and the number of daughter modes N ∼ 10<SUP>10</SUP>E<SUP>5/4</SUP><SUB>0,42</SUB>. The growth rate is approximately equal to the angular frequency of the primary mode times its dimensionless radial amplitude, δR/R<SUB>*</SUB> ≍ 0.002E<SUP>-½</SUP><SUB>0,42</SUB>. Although the daughter modes are limited by their own nonlinearities, collectively they absorb most of the primary mode's energy after a time ∼10ɛ<SUP>-1</SUP> provided E0 &gt; 10<SUP>40</SUP> ergs. This is orders of magnitude smaller than usual radiative damping time. In fact, nonlinear mode interaction may be the dominant damping process if E<SUB>0</SUB> ≥ 10<SUP>37</SUP> ergs. These results have obvious application to tidally captured main-sequence globular cluster stars of mass ≥ 0.5 M<SUB>sun</SUB>; the tidal energy is dissipated in the radiative core of the star in about a month, which is less than the initial orbital period. <P />Nonlinear mode coupling is a less efficient damping process for fully convective stars, which lack g-modes. In convective stars, most of the tidal energy is in the quadrupole f-modes, which nonresonantly excite high-order p-modes of degree 0, 2, and 4. The resultant short-wavelength waves are more efficiently dissipated. The nonlinear damping time for f-modes is shown to be proportional to 1/E<SUB>0</SUB>; this damping time is about 30 days for E<SUB>0</SUB> ≍ 10<SUP>45</SUP> ergs expected in tidal captures. However, at such a large energy the system is very nonlinear: 4-mode and higher order couplings are as important as 3-mode couplings.

High-order torsional couplings in the infrared spectrum of 3,3,3-trifluoropropene

Author Institution: Universit\{a}t Ulm, Abteilung f\{u}r Physikalische Chemie; Molecular Physics Division, National Institute of Standards and Technology

Theoretical study of intramolecular vibrational relaxation of acetylenic CH vibration for v=1 and 2 in large polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si

Quantum calculations are reported for the intramolecular vibrational energy redistribution and absorption spectra of the first two excited states of the acetylenic CH stretch vibration in the polyatomic molecules (CX3)3YCCH, where X=H or D and Y=C or Si. Using approximate potential energy surfaces, comparison is made with the corresponding recent experimental spectra. It is found that a model of intramolecular vibrational relaxation based on the assumption of sequential off-resonance transitions via third and fourth order vibrational couplings (as opposed to direct high order couplings) is in agreement with experimental results on spectral linewidths. In a semiclassical limit this type of relaxation corresponds to a dynamic tunneling in phase space. It is shown that the local density of resonances of third and fourth order, rather than the total density of states, plays a central role for the relaxation. It is found that in the Si molecule an accidental absence of appropriate resonances results in a bottleneck in the initial stages of relaxation. As a result, an almost complete localization of the initially prepared excitation occurs. It is shown that an increase of the mass alone of the central atom from C to Si cannot explain the observed difference in the C and Si molecules. The spectral linewidths were calculated with the Golden Rule formula after prediagonalization of the relevant vibrational states which are coupled in the molecule to the CH vibration, directly or indirectly. For the spectral calculations, in addition to the direct diagonalization, a modified recursive residue generation method was used, allowing one to avoid diagonalization of the transformed Lanczos Hamiltonian. With this method up to 30 000 coupled states could be analyzed on a computer with relatively small memory. The efficiency of C programming language for the problem is discussed.

Associative memories with short-range, higher order couplings

A study of recurrent associative memories with exclusively short-range connections is presented. To increase the capacity, higher order couplings are used. We study capacity and pattern completion ability of networks consisting of units with binary (±1) output. Results show that perfect learning of random patterns is difficult for very short coupling ranges, and that the average expected capacities (allowing small errors) in these cases are much smaller than the theoretical maximum, 2 bits per coupling. However, it is also shown that by choosing ranges longer than certain limit sizes, depending on network size and order, we can come close to the theoretical capacity limit. We indicate that these limit sizes increase very slowly with net size. Thus, couplings to at least 28 and 36 neighbors suffice for second order networks with 400 and 90,000 units, respectively. From simulations it is found that even networks with coupling ranges below the limit size are able to complete input patterns with more than 10% errors. Especially remarkable is the ability to correct inputs with large local errors (part of the pattern is masked). We present a local learning algorithm for heteroassociation in recurrent networks without hidden units. The algorithm is used in a multinet system to improve pattern completion ability on correlated patterns.

Higher-order coupling effects in low energy heavy-ion fusion reactions.

Higher-order couplings to inelastic excitations of surface vibrations can strongly affect the enhancement of heavy-ion fusion cross sections at sub-barrier energies. Detailed second-order calculations are presented for reactions between different nickel isotopes. The agreement with measured fusion cross sections is considerably improved with respect to conventional coupled channels calculations based on linear couplings.

Skyrmion-baryon phenomenology in the effective gauged chiral-SU(2) action approach

The phenomenology of the baryon-skyrmion is examined within the gauged chiral-SU(2) action approach developed recently by Brihaye, Pak and Rossi. The effective action incorporates the ρ, ω and A 1 vector mesons and obeys all (normal and anomalous) Ward identities of QCD, consistently with vector meson dominance. The approach realizes the chiral × hypercharge symmetry SU(2) L × SU(2) R × U(1) Y as a local gauge symmetry, modified by the addition of degenerate vector meson mass terms (breaking the symmetry from local to global) and of a gauged Wess-Zumino anomalous action, breaking the symmetry to SU(2) V × U(1) Y. We offer a general didactic presentation of the method and emphasize those aspects relating to the higher-order couplings and to the identification of currents. Detailed numerical investigations are carried out for the chiral soliton with respect to the classical field theory problem as well as the semi-classical quantization of isorotational zero modes. We treat first a truncated version where only ρ and ω are present and consider next, in classical approximation only, the complete version with ρ, ω and A 1 present. The results obtained are globally satisfactory, better for the classical mass and isoscalar observables than for the spin and isovector observables (Δ − N mass difference, μ v and g A). For a precise matching of predictions with experiment one cannot dispense with a readjustment of physical parameters F π and g. However, the amplitude of the readjustment needed are relatively mild (−15% for F π and 40% for g with respect to the meson phenomenology) and the improved fit to the nucleon properties is superior to that of the conventional Skyrme model.

Study of reaction asymmetries and spin orbit interaction of13C and11B in (12C,13C) and (12C,11B) reactions on208Pb

Angular distributions of neutron pick-up and proton stripping reactions in the interaction of12C on208Pb have been studied atE L =101 MeV with high accuracy using aQ3D magnetic spectrometer. Angular distributions of the single particle states are discussed in terms of reaction asymmetriesA ij (Θ). With these quantities the relative changes of the shapes of angular distributions can be studied in detail. The transferedl-value has been found to have a large effect on the shapes. For the case of13C an overall description of this quantity is obtained, if a spin-orbit interaction for13C is introduced with a sign which is opposite to that found in (14C,13C) reactions. For the case of11B the reaction asymmetries cannot be described by a spin-orbit interaction. The possible origin of the spin-orbit effects is discussed. The particular discrepancies to a simple DWBA description (without spin-orbit interaction) found in both the13C and11B angular distributions must be attributed to coupling effects in the initial channel, where the 2+ state of12C and 3− state of208Pb are excited, and to smaller extend to higher order couplings in the final channel.

Phonon effects in deep-level spectra of metals: Beyond the linear-screening and linear-coupling models

A priori calculations of phonon broadening of core levels in metals are presented. The effects of nonlinear screening and higher-order couplings are taken into account for the first time. The nonlinear screening effects are very important for Li and must be accounted for in order to obtain agreement with experiment.

Generalized reduction factors for the Jahn-Teller effect on a doublet

Formulae for the reduction factors q and p of the Jahn-Teller effect operating in an orbital doublet are suggested. These incorporate the effects of both the linear and higher-order couplings. Des formules pour les facteurs de réduction q et p de l'effet Jahn- Teller, opérant dans un doublet orbital, sont suggérées. Ces formules incorporent les effets des couplages linéaires aussi bien que ceux des ordres plus élevés/