Fermionic dispersion relations at finite temperature and non-vanishing chemical potentials in the minimal standard model

We calculate the fermionic dispersion relations in the minimal standard model at finite temperature in presence of non-vanishing chemical potentials due to the CP-asymmetric fermionic background. The dispersion relations are calculated for a vacuum expectation value of the Higgs field equal to zero (unbroken electroweak symmetry). The calculation is performed in the real time formalism of the thermal field theory at one-loop order in a general ζ gauge. The fermionic self-energy is calculated at leading order in temperature and chemical potential and this fact permits us to obtain gauge-invariant analytical expressions for the dispersion relations.     

Internal gravity waves in the Strait of Luzon: Dispersion studies using Fourier and continuous wavelet transforms

Investigation of the dynamics of internal gravity waves often includes the interrelationship between wave amplitudes, wave speeds, and wavelengths. These relationships are commonly thought of as dispersion relations. Because internal gravity waves are the result of nonlinear dynamics dispersion relations are a challenge to obtain in a quantitative sense. Model data for internal gravity waves in the Strait of Luzon are examined using Fourier and continuous wavelet transforms. Dispersion is qualitatively evident in the results and the investigation is extended to include quantitative assessment of the dispersion. The results are compared to results from Korteweg D’Vries theory. Good agreement is obtained for dispersion estimates using wavelet analysis and those from KdV theory.     

Rigorous sum rules and bounds on pion-pion scattering amplitudes with positivity

We derive the complete set of crossing symmetric forward pion-pion amplitudes with non-negative absorptive parts obeying twice-subtracted dispersion relations. We give a method to eliminate subtraction constants for these amplitudes by making a simultaneous use of subtracted dispersion relations for the amplitude and its inverse, and unitarity. We thus deduce from axiomatic field theory (i) lower bounds on forward real parts in terms of physical forward amplitudes, (ii) lower bounds on S- and P-wave scattering lengths in terms of forward amplitudes in any part of the physical region, (iii) sum rules on scattering lengths in terms of physical forward amplitudes which provide a complete test of forward dispersion relations, (iv) upper bounds on scattering lengths in terms of total cross sections and (v) absolute sum rule inequalities on total and forward differential cross sections in terms of the pion mass alone which provide new tests of dispersion relations not involving scattering lengths.     

Precision model independent determination of |Vub| from B --> pilnu

A precision method for determining |V(ub)| using the full range in q(2) of B --> pilnu data is presented. At large q(2) the form factor is taken from unquenched lattice QCD, at q(2) = 0 we impose a model independent constraint obtained from B --> pipi using the soft-collinear effective theory, and the shape is constrained using QCD dispersion relations. We find |V(ub)| = (3.54 +/- 0.170 +/- 0.44) x 10(-3). With 5% experimental error and 12% theory error, this is competitive with inclusive methods. Theory error is dominated by the input points, with negligible uncertainty from the dispersion relations.     

Exciting the GKP string at any coupling

We analyze the spectrum of excitations around the Gubser-Klebanov-Polyakov (GKP) rotating string in the long string limit and construct a parametric representation for their dispersion relations at any value of the string tension. On the gauge theory side of the AdS/CFT correspondence, i.e., in the planar N=4 super Yang-Mills theory, the problem is equivalent to finding the spectrum of scaling dimensions of large spin, single-trace operators. Their scaling dimensions are obtained from the analysis of the Beisert-Staudacher asymptotic Bethe ansatz equations, which are believed to solve the spectral problem of the planar gauge theory. We examine the resulting dispersion relations in various kinematical regimes, both at weak and strong coupling, and detail the matching with the Frolov-Tseytlin spectrum of transverse fluctuations of the long GKP string. At a more dynamical level, we identify the mechanism for the restoration of the SO(6) symmetry, initially broken by the choice of the Berenstein-Maldacena-Nastase vacuum in the Bethe ansatz solution to the mixing problem.     

Comparison of \pi K scattering in SU(3) chiral perturbation theory and dispersion relations

We establish the framework for the comparison of scattering amplitudes from SU(3) chiral perturbation theory with suitable dispersive representations which result from the combination of certain fixed-t dispersion relations with dispersion relations on hyperbolic curves. This allows for predictions for some combinations of low energy constants appearing in higher order calculations of chiral perturbation theory. Using a simple parametrization for the lowest partial waves, first estimates for some combinations are presented. Received: 6 December 2000 / Revised version: 13 February 2001 / Published online: 23 March 2001     

A study on the dispersions of piezoelectric plate with laser ultrasound measurement and theoretical modeling

This research is focused in the measurement and modeling for the dispersion relations of Lamb waves propagating in LiNbO(3) and LiTaO(3) plates. A theoretical model based on a stiffness matrix method with recursion computation algorism is used to provide numerical calculations for the dispersion relations. Also, a dry, noncontact laser ultrasound technique is used to measured dispersion multi-mode dispersion relations. For all the experiments, the measured dispersion curves show good agreement with the theoretical calculation, indicating the reliabilities in the measurement and modeling.     

Lattice effects in the quasiparticle dynamics and kinetics

In this work we present a full selfconsistent set of nonlinear equations which unifies the nonlinear elasticity theory equations, the Boltzmannn transport theory and the Maxwell equations for quasiparticles with arbitrary dispersion laws in nonstationarily deformed crystals with arbitrary (but linear) constitutive relations. Transformations to replace the Galilean ones are obtained, the quasiparticle mechanics in a Hamiltonian form is deduced, and a Boltzmann-type transport equation (valid in the whole Brillouin zone) is derived. The theory may be applied to metals, semiconductors, quantum crystals, low-dimensional structures etc. Received 20 October 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: dipushk@issp.bas.bg     

On the calculation of the bremsstrahlung in the region of the plasma frequency

On the basis of the classical theory of radiation produced in incomplete Coulomb interaction, a formula is derived for the coefficient of the bremsstrahlung of fully ionized plasma. In the region of rectilinear approximation a comparison is made with the results of the quantum formula derived from the Born approximation. Furthermore, the influence of dispersion upon the emission coefficient is taken into account; some relations for the region of dispersion are given.     

Ultraviolet modifications of dispersion relations in effective field theory

The existence of a fundamental ultraviolet scale, such as the Planck scale, may lead to modifications of the dispersion relations for particles at high energies in some scenarios of quantum gravity. We apply effective field theory to this problem and identify dimension-5 operators that do not mix with dimensions 3 and 4 and lead to cubic modifications of dispersion relations for scalars, fermions, and vector particles. Further we show that, for electrons, photons and light quarks, clock comparison experiments bound these operators at 10(-5)/M(Pl).     

Plasmons at the interface between a corrugated semiconductor film and a binary metallic superlattice

We investigate the minigaps of the dispersion relation of plasmon polaritons that propagate at the interface between a corrugated semiconductor film and a binary metallic superlattice. Minima of the reflectivity for p-polarized light are calculated and their frequencies are used to obtain the ‘optical’ dispersion relations which are compared with the corresponding electromagnetic dispersion curves, in the effective medium theory. Results show that the minigap enlarges with the corrugation strength.     

On the Role of the Results Obtained by the Analytical Theory of Elementary Particles

To prove that it is possible to obtain many results (such as the asymptotic relations of Pameranchuk type, Froissart inequality, Martin theorem, etc.) of the analytical theory of elementary particles in any theory where the ordinary analyticity of dispersion amplitude is replaced by a certain generalized analyticity (such as the p-analyticity of Poloji, the generalized analyticity of Vekua). Hence we cannot consider these results as criteria for the validity of the analyticity at high energies. Therefore, in order to check the analyticity we ought to establish the relations which can not be deduced from any generalized analyticity, except ordinary analyticity.     

Shear-horizontal waves in a rotated Y-cut quartz plate in contact with a viscous fluid

We study shear-horizontal (SH) waves in a crystal plate of rotated Y-cut quartz in contact with a semi-infinite viscous fluid. The crystal plate and the fluid are governed by the equations of anisotropic elasticity and the theory of Newtonian fluids. A transcendental equation that determines the dispersion relations of the waves is obtained. Approximate analytical solutions to the equation are presented for the case of low viscosity fluids and the case of long waves whose wavelength is much larger than the plate thickness. The effects of the fluid viscosity and density on the dispersion relations of the waves are examined. The results obtained are fundamental and useful to the understanding and design of acoustic wave fluid sensors for measuring fluid viscosity or density.     

Rigorous Analysis of Electromagnetic Wave Propagation in Cylindrical Dielectric Waveguide Array

Cylindrical Dielectric Waveguide Array(CDWA) should be considered as a kind of two-dimensionally periodic(2DP) medium. Based on the established rigorous theory for 2DP medium, a great amount of numerical results for CDWA were presented. Wave propagation in CDWA was analyzed in detail in this paper. Firstly, given the longitudinal wave vector (k _z=0), Brillouin dispersion relations between transverse wave vectors were analyzed when modulation coefficients or the rate of different dielectric areas in a unit cell varied. Interactions between space harmonics were also studied. Secondly, when the area of dielectric cylinder in the unit cell varied within a given range, CDWA dispersion relations were compared with Rectangle Dielectric Waveguide Array's, some interesting conclusions were obtained.     

Electromagnetic and fluctuation-electromagnetic forces of interaction of moving particles and nanoprobes with surfaces: A nonrelativistic consideration

The most complete nonrelativistic theory of dynamic fluctuation electromagnetic interactions between particles of various types (charges, dipoles, neutral atoms, nanoparticles) and the surfaces (flat or cylindrical) of a polarizable medium (the boundary of a solid) is reported for the first time. The theory is based on the application of the Maxwell equations and the formalism of fluctuation-dissipation relations. For a flat surface, effects of spatial dispersion are also taken into account. Papers of other authors are analyzed critically. The results of recent investigations in which dissipative fluctuational forces could be observed are considered briefly.     

On the applicability of Kramers-Kronig relations for ultrasonic attenuation obeying a frequency power law

In the recent literature concern has been raised regarding the validity of Kramers-Kronig relations for media with ultrasonic attenuation obeying a frequency power law. It is demonstrated, however, that the Kramers-Kronig dispersion relations for application to these types of media are available. The developed dispersion relations are compared with measurements on several liquids, and agreement is found to better than 1 m/s over the experimentally available bandwidth. A discussion regarding the validity of these dispersion relations, in particular how the dispersion relations relate to the so-called Paley-Wiener conditions, forms the conclusion.     

Quantum Theory of Surface Polaritons on a Rough Surface

In this paper, we present the quantum field theory of the surface phonon-polaritolis on a rough polar crystal surface. The dispersion relations of the surface phonon-polaritons and the dispersion relations of polariton leaking modes owing to the interaction between bulk TO mode with the surface effect and photons are derived. We also study the k-dependence of the electric field strength in each polariton branch. The numerical calculations for the dispersion relations and the k-dependence of the electric field strength are carried out for a stepped Gap surface. The results show that the surface roughness depressed the frequency of the surface phonon-polariton below its values in the absence of the surface roughness. For the frequencies of the polariton leaking modes, the photon-like one is enhanced by the surface roughness and the phonon-like one b depressed. Our evaluations also illustrate that the surface roughness introduces a strong dependence on the k-dependence of the electric field strength in each polariton branch.     

The Linear Analysis of Coaxial Helical-Groove Slow-Wave Structure

The coaxial helical-groove slow-wave structure is a new-type high power circuit. The dispersion equation of this circuit with an annular electron beam is obtained according to self-consistent field theory. The computation results of the hot dispersion equation show the relations between electron beam parameters and the small signal gain. The presented analysis will be useful for the design of the TWT with coaxial helical-groove circuit.