Perturbation Formalism Research Articles

Numerical tests of a new molecule-dependent momentum transport equation

It is shown that a new incompressible fluid equation is obtained by inclusion of a new dimensionless coupling parameter in the momentum transport equation derived in [L. Jirkovsky, L. Bo-ot, Momentum transport equation for the fluids using projection–perturbation formalism and onset of turbulence, Physica A 352 (2005) 241–251] from the Boltzmann kinetic equation where the Boltzmann collision integral includes inelastic interactions of quantum origin among the particles of the fluid. Numerical results from the equation for the plane and circular Poiseuille flows are consistent with the observations. The numerical tests also manifest a difference in the onset of turbulence between the flat plates and the circular pipe flow systems. Although all obtained velocity profiles are flattened at the center–a feature of turbulence–the results demonstrate greater stability of the velocity profiles in the circular pipe flow.

Fully unintegrated parton correlation functions and factorization in lowest-order hard scattering

Motivated by the need to correct the potentially large kinematic errors in approximations used in the standard formulation of perturbative QCD, we reformulate deeply inelastic lepton-proton scattering in terms of gauge-invariant, universal parton correlation functions which depend on all components of parton four-momentum. Currently, different hard QCD processes are described by very different perturbative formalisms, each relying on its own set of kinematical approximations. In this paper we show how to set up formalism that avoids approximations on final-state momenta, and thus has a very general domain of applicability. The use of exact kinematics introduces a number of significant conceptual shifts already at leading order, and tightly constrains the formalism. We show how to define parton correlation functions that generalize the concepts of parton density, fragmentation function, and soft factor. After setting up a general subtraction formalism, we obtain a factorization theorem. To avoid complications with Ward identities, the full derivation is restricted to Abelian gauge theories; even so, the resulting structure is highly suggestive of a similar treatment for non-Abelian gauge theories.

Predicted Doppler shifts induced by ocean surface wave displacements using asymptotic electromagnetic wave scattering theories

Sea surface motions can produce different measured Doppler shifts with respect to instrumental configurations (incidence angle, electromagnetic wavelength, polarization). Under Gaussian statistics for the sea surface elevation and in the general framework of asymptotic theories for ocean surface electromagnetic wave scattering, Doppler shifts can be predicted. The small-slope, Kirchhoff, local curvature and resonant curvature approximations are compared in the backscatter configuration. Predicted Doppler shifts for Kirchhoff and small-slope approximations in co-polarized configuration are insensitive to the polarization state. On the other hand, the local and resonant curvature solutions, through a phase perturbation formalism, yield to significant differences between co-polarized predicted Doppler shifts. Comparisons with data are shown to confirm the polarization and wind speed sensitivities.

Some Formal Aspects of the Theory of Intermolecular Interactions and of the BSSE Problem

Some results of mathematical character concerning the theory of intermolecular interactions and the BSSE problem are presented. It is shown that the concept of complete basis set may be introduced for intermolecular potential surfaces only by considering explicitly the limiting process in which the basis sets of both monomers approach completeness simultaneously. That does not lead to any overcompleteness problem if we do not postulate the existence of two complete basis sets from the outset. The intimate connection between the BSSE and the differences of some biorthogonal integrals and their "original" counterparts is also discussed. The operator of BSSE is given in terms of such differences. It is shown that in a special case, when only the overlap of the occupied orbitals is considered, the "bi-expectation" value of the energy coincides with the conventional expectation value for the single determinant wave function built up of the unperturbed orbitals of the individual monomers. It is discussed, by using a model of the biorthogonal perturbation theory, why the conceptually fully different a priori (CHA) and a posteriori (CP) schemes of BSSE correction usually give very close numerical results. (The necessary biorthogonal perturbation formalism is developed in the Appendices.) The results give justification for the additivity assumptions inherent in the CP method.

Quantification of discreteness effects in cosmologicalN-body simulations. II. Evolution up to shell crossing

We apply a recently developed perturbative formalism which describes the evolution under their self-gravity of particles displaced from a perfect lattice to quantify precisely, up to shell crossing, the effects of discreteness in dissipationless cosmological $N$-body simulations. We give simple expressions, explicitly dependent on the particle density, for the evolution of power in each mode as a function of redshift. For typical starting redshifts the effect of finite particle number is to slow down slightly the growth of power compared to that in the fluid limit (e.g., by about 10% at half the Nyquist frequency), and to induce also dispersion in the growth as a function of direction at a comparable level. In the limit that the initial redshift tends to infinity, at fixed particle density, the evolution in fact diverges from that in the fluid limit (described by the Zeldovich approximation). Contrary to widely held belief, this means that a simulation started at a redshift much higher than the redshift of shell crossing actually gives a worse, rather than a better, result. We also study how these effects are modified when there is a small-scale regularization of the gravitational force. We show that such a smoothing may reduce the anisotropy of the discreteness effects, but it then increases their average effect. This behavior illustrates the fact that the discreteness effects described here are distinct from those usually considered in this context, due to two-body collisions. Indeed the characteristic time for divergence from the collisionless limit is proportional to ${N}^{2/3}$, rather than $N/\mathrm{log}N$ in the latter case.

Non-linear interaction of waves in prestressed material

Interaction of two counterpropagating ultrasonic waves in an inhomogeneously prestressed elastic material (a structural element) with quadratic non-linearity is studied theoretically by using the perturbative formalism. The analytical solution that describes wave–wave, wave–material and wave–prestress non-linear interaction is derived. This rather cumbersome solution is studied in the case of a harmonic boundary condition in the material (specimen) subjected to two-parametric inhomogeneous prestressed state. The model problems are solved and the influence of the prestress on the wave interaction is cleared up. Resulting oscillations on two parallel boundaries of the material are prestress sensitive. It is proposed to use boundary oscillation data for non-destructive characterization of inhomogeneous prestressed state.

Emission and absorption noise in the fractional quantum Hall effect

We compute the high-frequency emission and absorption noise in a fractional quantum Hall effect (FQHE) sample at arbitrary temperature. We model the edges of the FQHE as chiral Luttinger liquids, and we use the nonequilibrium perturbative Keldysh formalism. We find that the nonsymmetrized high-frequency noise contains important signatures of the electron-electron interactions that can be used to test the Luttinger liquid physics, not only in FQHE edge states but possibly also in other one-dimensional systems such as carbon nanotubes. In particular, we find that the emission and absorption components of the excess noise (defined as the difference between the noise at finite voltage and at zero voltage) are different in an interacting system, as opposed to the noninteracting case when they are identical. We study the resonance features which appear in the noise at the Josephson frequency (proportional to the applied voltage), and we also analyze the effect of the distance between the measurement point and the backscattering site. Most of our analysis is performed in the weak-backscattering limit, but we also compute and discuss briefly the high-frequency noise in the tunneling regime.

Grazing-incidence small-angle x-ray scattering from dense packing of islands on surfaces: Development of distorted wave Born approximation and correlation between particle sizes and spacing

This paper is devoted to the analysis methodology of grazing-incidence small-angle x-ray scattering from dense assemblies of islands on a surface. To interpret the experimental data for increasing coverage, (i) the distorted wave Born approximation (DWBA) formalism has been extended to include the exact profile of electronic density, i.e., the fuzziness of the interface, and (ii) the scaling of the Vorono\"{\i} cell size of each particle with its size has been introduced in the scattering formalism. Multiple scattering effects in the perpendicular direction, i.e., along the emergence angle, are treated within the DWBA using the full perpendicular profile of refraction index as a reference state of the perturbation formalism and not simply the bare substrate. Thus, the average along the surface of the perturbation due to the particles or the holes in between is zero. It is shown that the concept of island form factor is still valid and includes, in a continuous integral, scattering events from upward to downward propagating waves (and vice versa) in the graded interface. Contrary to the case of multiple scattering on the bare substrate, the shape of Yoneda's peak as well as the location and sharpness of the perpendicular interference fringes depend on the coverage for monodisperse particles, or more generally, on the embedding profile of refraction index. In the parallel direction, i.e., along the surface plane, a one dimensional model based on the paracrystal is proposed to include correlations between the size and the spacing of the particles. In this model, the interplay between coherent and incoherent scattering can lead to a hollow of scattered intensity between the specular rod and the correlation peak, as experimentally observed. This size-spacing correlation approximation goes beyond the commonly used approximations of scattering from a dense collection of particles, i.e., (i) the decoupling approximation characterized by a random disorder and by a too intense incoherent scattering and (ii) the convenient local monodisperse approximation which relies on a description of the scattering system as a set of monodisperse domains, which is not physically sound in many cases. The three approximations are compared on a physically relevant case. In a following experimental paper [R. Lazzari et al., Phys. Rev. B 76, 125412 (2007)], these models are applied to the analysis of the $\mathrm{Au}∕\mathrm{Ti}{\mathrm{O}}_{2}(110)$ growth mode.

Production of Magnetic Energy by Macroscopic Turbulence in GRB Afterglows

Afterglows of gamma-ray bursts are believed to require magneticfields much stronger than that of the compressed preshockmedium.Asanalternativetomicroscopicplasmainstabilities,weproposeamplificationofthefieldbymacroscopicturbulenceexcitedbytheinteractionoftheshockwithaclumpypreshockmedium,forexample,astellarwind. Using a recently developed formalism for localized perturbations to an ultrarelativistic shock, we derive constraints on thelengthscale,amplitude,andvolumefillingfactorof densityclumpsrequiredtoproduceagivenmagneticenergyfractionwithintheexpansiontimeoftheshock,assumingthattheenergyinthefieldachievesequipartionwiththeturbulence. StrongerandsmallerscaleinhomogeneitiesarerequiredforlargershockLorentzfactors.Hence,itislikelythatthe magnetic energy fraction evolves as the shock slows. This could be detected by monitoring the synchrotron cooling frequency if the radial density profile ahead of the shock, smoothed over clumps, is known. Subject headingg gamma rays: bursts — hydrodynamics — magnetic fields — shock waves — turbulence

Effect of reconstruction-induced strain on the reflectance difference spectroscopy of GaAs (001) aroundE1andE1+Δ1transitions

We report measurements of reflectance difference (RD) spectra for $c(4\ifmmode\times\else\texttimes\fi{}4)$ and $(2\ifmmode\times\else\texttimes\fi{}4)$ reconstructed (001) surfaces of GaAs. Surface dimers induce an inhomogeneous orthorhombic strain field that penetrates several monolayers into the crystal. The thickness $d$ of this strained region is smaller than the penetration depth $L$ of the probing light, and an inhomogeneous anisotropy formalism can be used. The dielectric function of GaAs at room temperature can be described by a discrete (Lorentzian) excitonic line shape. For the contribution of the region near the surface to the optical response, the excitonic response should be at least partly quenched because of the electric field present near the surface. Thus, a one-electron contribution (logarithmic line shape) may have to be used to fit the RD spectra. By using an inhomogeneous perturbation formalism and a logarithmic line shape, we have been able to isolate the strain component induced by the dimers around ${E}_{1}$ and ${E}_{1}+{\ensuremath{\Delta}}_{1}$ critical points. We also inferred that the RD spectra include a component related to surface roughness.

Dynamics of charged fluids and 1/ℓ perturbation expansions

Some features of the calculation of fluid dynamo systems (spherically symmetric α2-dynamos) in magnetohydrodynamics are studied, the problem connected with the presence of mixed (Robin) boundary conditions is addressed and a new treatment for it is proposed. The perturbation formalism of large-ℓ expansions is shown to be applicable and its main technical steps are outlined.

How far away is far enough for extracting numerical waveforms, and how much do they depend on the extraction method?

We present a method for extracting gravitational waves from numerical spacetimes which generalizes and refines one of the standard methods based on the Regge–Wheeler–Zerilli perturbation formalism. At the analytical level, this generalization allows a much more general class of slicing conditions for the background geometry, and is thus not restricted to Schwarzschild-like coordinates. At the numerical level, our approach uses high-order multi-block methods, which improve both the accuracy of our simulations and of our extraction procedure. In particular, the latter is simplified since there is no need for interpolation, and we can afford to extract accurate waves at large radii with only little additional computational effort. We then present fully nonlinear three-dimensional numerical evolutions of a distorted Schwarzschild black hole in Kerr–Schild coordinates with an odd parity perturbation and analyse the improvement that we gain from our generalized wave extraction, comparing our new method to the standard one. In particular, we analyse in detail the quasinormal frequencies of the extracted waves, using both methods. We do so by comparing the extracted waves with one-dimensional high resolution solutions of the corresponding generalized Regge–Wheeler equation. We explicitly see that the errors in the waveforms extracted with the standard method at fixed, finite extraction radii do not converge to zero with increasing resolution. We find that even with observers as far out as R = 80M—which is larger than what is commonly used in state-of-the-art simulations—the assumption in the standard method that the background is close to having Schwarzschild-like coordinates increases the error in the extracted waves considerably. Furthermore, those errors are dominated by the extraction method itself and not by the accuracy of our simulations. For extraction radii between 20M and 80M and for the resolutions that we use in this paper, our new method decreases the errors in the extracted waves, compared to the standard method, by between one and three orders of magnitude. In a general scenario, for example a collision of compact objects, there is no precise definition of gravitational radiation at a finite distance, and gravitational wave extraction methods at such distances are thus inherently approximate. The results of this paper bring up the possibility that different choices in the wave extraction procedure at a fixed and finite distance may result in relative differences in the waveforms which are actually larger than the numerical errors in the solution.

Nonequilibrium perturbative formalism and spectral function for the Anderson model

The present work is based on the nonequilibrium perturbative formalism. There the self-energies are derived up to the fourth-order. Consequently, it proves that the nonequilibrium (real-time) perturbative expansion can be connected with the Matsubara imaginary-time perturbative expansion for equilibrium. As the numerical results, the Kondo resonance still disappears for bias voltage exceeding the Kondo temperatures, as observed in experiments of two terminal systems.

High-order gauge-invariant perturbations of a spherical spacetime

We construct a covariant and gauge-invariant framework to deal with arbitrary high-order perturbations of a spherical spacetime. It can be regarded as the generalization to high orders of the Gerlach and Sengupta formalism for first-order nonspherical perturbations. The Regge-Wheeler-Zerilli harmonics are generalized to an arbitrary number of indices and a closed formula is deduced for their products. An iterative procedure is given in order to construct gauge-invariant quantities up to any perturbative order. Focusing on second-order perturbation theory, we explicitly compute the sources for the gauge invariants as well as for the evolution equations.

The strange parton distribution of the nucleon: global analysis and applications

The strangeness degrees of freedom in the parton structure of the nucleon are explored in the global analysis framework, using the new CTEQ6.5 implementation of the general mass perturbative QCD formalism of Collins. We systematically determine the constraining power of available hard scattering experimental data on the magnitude and shape of the strange quark and anti-quark parton distributions. We find that current data favor a distinct shape of the strange sea compared to the isoscalar non-strange sea. A new reference parton distribution set, CTEQ6.5S0, and representative sets spanning the allowed ranges of magnitude and shape of the strange distributions, are presented. Some applications to physical processes of current interest in hadron collider phenomenology are discussed.

Gravitational waves from nonlinear couplings of radial and polar nonradial modes in relativistic stars

The postbounce oscillations of newly-born relativistic stars are expected to lead to gravitational-wave emission through the excitation of nonradial oscillation modes. At the same time, the star is oscillating in its radial modes, with a central density variation that can reach several percent. Nonlinear couplings between radial oscillations and polar nonradial modes lead to the appearance of combination frequencies (sums and differences of the linear mode frequencies). We study such combination frequencies using a gauge-invariant perturbative formalism, which includes bilinear coupling terms between different oscillation modes. For typical values of the energy stored in each mode we find that gravitational waves emitted at combination frequencies could become detectable in galactic core-collapse supernovae with advanced interferometric or wideband resonant detectors.

Fourth GenerationCPViolation Effects onB→Kπ,φK, andρKin Next-to-Leading-Order Perturbative QCD

We study the effect from a sequential fourth generation quark on penguin-dominated two-body nonleptonic B meson decays in the next-to-leading order perturbative QCD formalism. With an enhancement of the color-suppressed tree amplitude and possibility of a new CP phase in the electroweak penguin amplitude, we can account better for A(CP)(B(0)-->K+ pi-)-A(CP)(B+-->K+ pi0). Taking |V(t's)V(t'b)| approximately 0.02 with a phase just below 90 degrees, which is consistent with the b-->sl+ l- rate and the B(s) mixing parameter Deltam(B)(s), we find a downward shift in the mixing-induced CP asymmetries of B(0)-->K(S)(pi 0) and phi(K)(S). The predicted behavior for B(0)-->rho(0)(K)(S) is opposite.

Theoretical investigation of the relationship between spin torque and magnetoresistance in spin-valves and magnetic tunnel junctions

A theoretical study is presented concerning the relationship between spin transfer torque and absolute current-perpendicular-to-plane magnetoresistance in metallic spin-valves (SV) and magnetic tunnel junctions. In a first step, using Valet and Fert Boltzmann-like theory extended to any metallic magnetic multilayers with non-collinear magnetizations, linear relationships between spin torque and absolute current-perpendicular-to-plane giant magnetoresistance are derived numerically, when varying the parameters of the structure one by one. The obtained results are compared with an extension of J.C. Slonczewski's circuit theory. The latter model gives an analytical expression of this linear dependence. In a second step, using an out-of-equilibrium perturbation formalism (Keldysh technique), we study the tunnel magnetoresistance (TMR) dependence of the spin torque amplitude in magnetic tunnel junctions when varying the parameters one by one in the junction. Once again, linear dependences are obtained, with different characteristics when the TMR vanishes. It is shown that these two equivalent behaviours are associated with different origins of the spin torque.

Perturbative diffusion theory formalism for interpreting temporal light intensity changes during laser interstitial thermal therapy

In an effort to understand dynamic optical changes during laser interstitial thermal therapy (LITT), we utilize the perturbative solution of the diffusion equation in heterogeneous media to formulate scattering weight functions for cylindrical line sources. The analysis explicitly shows how changes in detected interstitial light intensity are associated with the extent and location of the volume of thermal coagulation during treatment. Explanations for previously reported increases in optical intensity observed early during laser heating are clarified using the model and demonstrated with experimental measurements in ex vivo bovine liver tissue. This work provides an improved understanding of interstitial optical signal changes during LITT and indicates the sensitivity and potential of interstitial optical monitoring of thermal damage.

Effects of band structure and quantum interference on the differential conductance ofinfinite metallic single-wall carbon nanotubes

Using a π-orbital tight-binding (TB) model within a perturbative formalism, the effects ofsubstitutional impurities on the conductance of infinite metallic single-wall carbonnanotubes (MSWCNTs) are studied. The perturbative scheme is based on the energydissipation of electrons travelling through the nanotube. A general expression for thedifferential conductance (DC) is presented, and scattering processes are investigated. It isdemonstrated how the DC depends sensitively on the nature of the electronic bandstructure and velocity of carriers moving in the nanotube. We have shown that thequantum interference (QI) of electronic waves scattered by impurities plays a meaningfulrole. In particular, for the case of a couple of impurities the DC exhibits periodicoscillations comprising both positive and negative values. The negative differentialconductance (NDC) stemming from the QI and rotational symmetry selection ruleis very sensitive to the relative distance and symmetry of two impurities. Thissignature is absent for the case of a single impurity. In fact, the NDC can beattributed to the zero-temperature/elastic weak-localization correction to theconductance. As a result, the faster/higher and slower/shorter oscillations can theneffectively be achieved by metallic zigzag and armchair nanotubes, respectively.A corrigendum for this article has been published in 2007 J. Phys.: Condens. Matter 19 469001