Dressed ion acoustic solitary waves in quantum plasmas with two polarity ions and relativistic electron beams

A theory for dressed quantum ion acoustic waves (QIAWs), which includes higher-order corrections when QIAWs are investigated by the reductive perturbation method, is presented for unmagnetized plasmas containing positive and negative ions and weakly relativistic electron beams. The properties of the QIAWs are investigated using a quantum hydrodynamic model, from which a Korteweg–de Vries equation is derived using the reductive perturbation method. An equation including higher-order dispersion and nonlinearity corrections is also derived, and the physical parameter space is discussed for the importance of these corrections.     

Corrections to the Casimir–Polder potential arising from electric octupole coupling

ABSTRACT

Molecular QED theory is employed to derive a generalised formula for the dispersion potential between two molecules with mixed electric multipole polarisability tensors of arbitrary order at each centre. This expression is used to readily extract the pair energy shift between an electric dipole polarisable molecule and a mixed electric dipole–octupole polarisable one, and that between two mixed electric dipole–octupole polarisable species. This is done to see whether these interaction energies give rise to higher-order corrections to the Casimir–Polder potential, as was found in the previously calculated case of the dispersion energy shift between an electric dipole polarisable molecule and an electric octupole polarisable one. Interestingly, for orientationally averaged species, both of the computed interaction energies are independent of the octupole weight-3 term, are retarded, and may be interpreted as higher-order corrections in the fine structure constant to the leading dipole–dipole dispersion potential.     

The effects of vibration-rotation interaction on the quadrupole hyperfine structure of molecular rotational levels

By using a contact transformation method similar to that commonly employed when determining higher-order corrections to the harmonic oscillator and rigid rotor energy levels of molecules, analogous centrifugal distortion and anharmonic corrections to the nuclear quadrupole coupling energies have been obtained for molecules containing one quadrupolar nucleus. The J, K dependence and v, l dependence of these higher-order corrections to the quadrupole hyperfine energies can be cast in a form which is remarkably similar to the form taken for ordinary vibrational and rotational energy corrections, a result which was not evident from earlier partial treatments of this general problem. Results are obtained here for asymmetric top, symmetric top, spherical top, and linear molecules.     

Multi-instantons and exact results III: Unification of even and odd anharmonic oscillators

This is the third article in a series of three papers on the resonance energy levels of anharmonic oscillators. Whereas the first two papers mainly dealt with double-well potentials and modifications thereof [see J. Zinn-Justin, U.D. Jentschura, Ann. Phys. (N.Y.) 313 (2004) 197 and 269], we here focus on simple even and odd anharmonic oscillators for arbitrary magnitude and complex phase of the coupling parameter. A unification is achieved by the use of PT-symmetry inspired dispersion relations and generalized quantization conditions that include instanton configurations. Higher-order formulas are provided for the oscillators of degrees 3 to 8, which lead to subleading corrections to the leading factorial growth of the perturbative coefficients describing the resonance energies. Numerical results are provided, and higher-order terms are found to be numerically significant. The resonances are described by generalized expansions involving intertwined nonanalytic exponentials, logarithmic terms and power series. Finally, we summarize spectral properties and dispersion relations of anharmonic oscillators, and their interconnections. The purpose is to look at one of the classic problems of quantum theory from a new perspective, through which we gain systematic access to the phenomenologically significant higher-order terms.     

Divergence-free WKB theory

We present a divergence-free WKB theory, which is a new semiclassical theory modified by nonperturbative quantum corrections. Conventionally, the WKB theory is constructed upon a trajectory that obeys the bare classical dynamics expressed by a quadratic equation in momentum space. Contrary to this, the divergence-free WKB theory is based on a higher-order algebraic equation in momentum space, which represents a dressed classical dynamics. More precisely, this higher-order algebraic equation is obtained by including quantum corrections to the quadratic equation, which is the bare classical limit. An additional solution of the higher-order algebraic equation enables us to construct a uniformly converging perturbative expansion of the wavefunction. Namely, our theory removes the notorious divergence of wavefunction at a turning point from the WKB theory. Moreover, our theory is able to produce wavefunctions and eigenenergies more accurate than those given by the traditional WKB method. In addition, the divergence-free WKB theory that is based on the cubic equation allows us to construct a uniformly valid wavefunction for the nonlinear Schrödinger equation (NLSE). A recent short letter [T. Hyouguchi, S. Adachi, M. Ueda, Phys. Rev. Lett. 88 (2002) 170404] is the opening of the divergence-free WKB theory. This paper presents full formalism of this theory and its several applications concerning wavefunction and eigenenergy to show that our theory is a natural extension of the traditional WKB theory that incorporates nonperturbative quantum corrections.     

Electrical properties of KTiOPO4 single crystal in the temperature range from −100 °C to 100 °C

The electrical property of a KTiOPO₄ single crystal was studied by means of a dielectric spectroscopy method in the temperature range from −100 to 100 °C. Dielectric dispersion began at a temperature, T_S=−80 °C. It is believed that this dielectric dispersion is related to the ionic hopping conduction, which arises mainly from the jumping of K⁺ ions. The activation energy concerned with hopping conduction is E_a∼0.20 eV above T_S. T_S=−80 °C can be the minimum temperature for the hopping K⁺ ion.     

Femto-Second Transform Limited Pulse Generation with Higher Order Dispersion Effects for Dispersion-Shifted Optical Communication System

The paper deals with the influence of higher-order effects of dispersion on the femto-second transform limited pulse generation by compensating for linear chirp of self-phase modulation spectra in the dispersion-shifted fibers. It has been shown that the minimum propagation length with first-order dispersion term is 23 m, as reported earlier. If the higher-order dispersion effects are taken into consideration, this length is reduced to 11.5 m. With compensation of the first-order dispersion term, this length can be enhanced to 6.8161 × 10³ km. This length can further be improved to 6.0343 × 10⁹ km by compensation of first- and second-order dispersion terms together. The minimum pulse width and linewidth product without dispersion, with dispersion including higher-order dispersion effects, and with dispersion compensation, is found to be 0.44, 0.4418, and 0.4411, respectively.     

Femto-Second Transform Limited Pulse Generation with Higher Order Dispersion Effects for Dispersion-Shifted Optical Communication System

The paper deals with the influence of higher-order effects of dispersion on the femto-second transform limited pulse generation by compensating for linear chirp of self-phase modulation spectra in the dispersion-shifted fibers. It has been shown that the minimum propagation length with first-order dispersion term is 23 m, as reported earlier. If the higher-order dispersion effects are taken into consideration, this length is reduced to 11.5 m. With compensation of the first-order dispersion term, this length can be enhanced to 6.8161 × 10³ km. This length can further be improved to 6.0343 × 10⁹ km by compensation of first- and second-order dispersion terms together. The minimum pulse width and linewidth product without dispersion, with dispersion including higher-order dispersion effects, and with dispersion compensation, is found to be 0.44, 0.4418, and 0.4411, respectively.     

Dispersion characteristics of complex refractive-index planar slab optical waveguide by using finite element method

In this paper, finite element method (FEM) mode analyses of planar slab optical waveguide having complicated refractive index profile are presented. We try to estimate the dispersion graph, mode cut-off condition, group delay and waveguide dispersion for the case of α-power and chirped-type refractive index profile. In order to obtain the more accurate result, we have derived the higher-order polynomial, which establishes the suitable relationship between b and V for different profile of optical waveguide. On the basis of the derived polynomials, the waveguide dispersion is analyzed for different type of refractive index profile waveguide. Our study shows that the waveguide dispersion can be substantially reduced when we deployed the optical waveguide having linearly chirped-type refractive index profile. Earlier too, the arbitrary refractive index profile has been analyzed but to the best of our knowledge chirped-type refractive index profile has not been analyzed till date for the case of planar slab optical waveguide.     

Manifestly supersymmetric O(α′) superstring corrections in new D = 10, N = 1 supergravity Yang-Mills theory

A systematic procedure in superspace to derive the O(α′) tree-level superstring corrections to the new D = 10, N = 1 (dual) supergravity Yang-Mills system is established. All the tree-level O(α′) corrections in the closed supersymmetry transformation laws are presented explicitly. These O(α′) corrections are regarded as a generalization of “matter” couplings in D = 10, N = 1 supergravity. The advantage of the superspace approach, based on superspace Bianchi identities, in comparison with the component formulation is elucidated. This new method is applicable to all anomaly-free D ⩽ 10 non-maximal supergravity theories, which utilize the Green-Schwarz mechanism. It also provides a way of introducing general higher-order powers of curvature tensors in D ⩽ 10 supergravity theories.     

Corrections to Weinberg's pion-pion scattering lengths

We derive twice subtracted dispersion sum rules for theππ scattering lengths. The subtraction constants are the Weinberg values, and the dispersion integrals yield small corrections in good agreement with other authors.     

Perturbative versus condensate effects in super-heavy quarkonia

The perturbative and non-perturbative corrections to the Balmer spectrum in super-heavy quarkonia are compared. The leading perturbative contribution is due to the asymptotic freedom correction to the Coulomb potential, and vanishes extremely slowly with increasing quark mass m. We compare different “optimal” choices for the scale at which α_s should be evaluated for use in the Balmer formula. The leading non-perturbative correction, which is thought to be due to the presence of a gluon condensate, only becomes appreaciable for states having a size larger than about 0.1 fm. At this scale α_s is already so large that it becomes very difficult to distinguish the non-perturbative corrections from the higher-order perturbative ones.     

On shell,subtracted dispersion relations and low energy theorems from current algebra

A method discussed in an earlier paper is applied to the case of ππ and πN scattering and to electroproduction. As an example we derive for the ππ scattering amplitude a subtracted, covariant on-shell dispersion relation in which the subtraction polynomial is determined by the corresponding low energy theorem plus possibly small corrections. We also show how this same method may be applied to the derivation of low energy theorems.     

A.c. conductivity in AsF5 doped polyphenylacetylene (PPA)

The a.c. conductivity of semiconducting cis-cisoid polyphenylacetylene (PPA) pellets has been studied at temperatures between 230 and 290 K and frequencies, ?, from 37 to 10⁵ Hz. The a.c. conductivity (σ_a.c.) is found to be strongly temperature dependent. σ_a.c. is proportional to ?^s with s varying from 0.45 to 0.75 as temperature is raised from 230 to 290 K. Both frequency dispersion and strong temperature dependence of σ_a.c. are best explained by the mechanism of hopping conduction in the band-tails.     

High-energy limit of massless Dirac fermions in multilayer graphene using magneto-optical transmission spectroscopy

We have investigated the absorption spectrum of multilayer graphene in high magnetic fields. The low-energy part of the spectrum of electrons in graphene is well described by the relativistic Dirac equation with a linear dispersion relation. However, at higher energies (>500 meV) a deviation from the ideal behavior of Dirac particles is observed. At an energy of 1.25 eV, the deviation from linearity is approximately 40 meV. This result is in good agreement with the theoretical model, which includes trigonal warping of the Fermi surface and higher-order band corrections. Polarization-resolved measurements show no observable electron-hole asymmetry.     

Investigations on power penalty at different spectral width using small signal analysis with higher-order dispersion

In this paper, a modified small signal analysis for power penalty at different spectral width of the light source has been investigated by incorporating the higher-order dispersion parameters. Further, we have analyzed the individual and combined effects of second- and third-order dispersion parameter on power penalty at different spectral line widths. The results have been reported over the range of 10-1000 km by considering the impact of individual and the combined higher-order dispersion terms. It has been observed that by reducing the spectral line width of the light source, the power required at the receiver can be minimized. The power penalty is further reduced if only third-order dispersion parameter is considered. Further, the transmitter distance can be maximized if the spectral width of the light reduces to 100 kHz.     

Hopping conduction in modulated superionics

The dynamics of a lattice gas model within a hopping limit in the presence of a structure modulation is studied. It is found that above a given critical value U_c of the modulating potential extra modes due to oscillations of the occupation numbers appear. In particular, it is shown that in the case of superionic conductors these are responsibilities for the peculiar dispersion of the microwave conductivity.     

Hopping conductivity and weak localization in two-dimensional disordered systems

The low temperature dependence of hopping conductivity σ(T) in 2d-DS with weak localization of electron states is investigated. Hopping between neighbouring localized states is suggested and a power law for σ(T) is obtained. Coulomb effects are shown to be negligible for this process. The transition from the logarithmic T dependence and to the exponential Mott's law is discussed. The density distribution of localized electron states is proved to be exponential. The dielectric permeability ?′(ω) is found to be proportional to |ω|^?1 in the field of validity of the logarithmic corrections.     

Two-electron self-energy contribution to the ground-state energy of helium-like ions

The two-electron self-energy contribution to the ground-state energy of helium-like ions is calculated both for a point nucleus and an extended nucleus in a wide interval of Z. All the two-electron contributions are compiled to obtain most accurate values for the two-electron part of the ground-state energy of helium-like ions in the range Z = 20–100. The theoretical value of the ground-state energy of ²³⁸U⁹⁰⁺, based on currently available theory, is evaluated to be −261382.9(8) eV, without higher-order one-electron QED corrections.