Long-wavelength Approximation Research Articles

Longitudinal and transverse components of excitons in a spherical quantum dot

Exciton states confined in a spherical quantum dot (QD) are studied in a weak confinement regime with the consideration of the electron-hole exchange interaction and induced surface charge density. Except for special cases, most exciton states are longitudinal (L)--transverse (T) mixed modes. With an increase of radius, the LT mixed modes approach bulk L, T, and surface (S) modes. When the energies of LT mixed modes get close to that of the S mode, they acquire considerable amount of S-mode character. It is demonstrated that the effect of the surface charge density does not affect the L-mode exciton confined in an arbitrary shape. Within the long-wavelength approximation, one-photon transitions toward the pure L and T modes are forbidden, and for other states the oscillator strengths per unit volume become maximum around the energy of the S mode.

Layer-induced elastic anisotropy Part 2: inversion of compound parameters to constituent parameters

In Part 1 of this paper (Helbig, 1998 - Rev. Bras. Geof. 16 (2<FONT FACE=Symbol>-</FONT>3):103<FONT FACE=Symbol>-</font>114) it was shown that a medium consisting of a periodic sequence of layers is, in the long-wavelength approximation, equivalent to a homogeneous compound medium with elastic parameters that are generalized averages of the constituents' stiffnesses. Though the matrix-algorithm described in Part 1 works with anisotropic constituents, the most interesting application is to layer sequences with isotropic constituents, i.e., to transversely isotropic (TI) compound media. Part 2 discusses the possibility to obtain information about the (thin-layer) constituents from the properties of the compound medium. Though every periodic sequence of isotropic layers results in a TI medium, the reverse is not true: there are TI media that cannot be "modeled" by a periodic sequence of isotropic layers. Those that can be modeled can be inverted to layer sequences that result in precisely the observed anisotropy. This inversion is not unique, but it constrains the possibilities. The critical tool to determine the possibility of modeling a TI medium is the concept of stability. Unstable compound media <FONT FACE=Symbol>-</FONT>that release energy on being deformed <FONT FACE=Symbol>-</FONT> would not exist. However, for inversion we must insist that not only the compound medium, but also the potential constituents are stable. In preparing a catalog that covers all possible media, instability is the boundary beyond which the calculation becomes meaningless. Inversion means to determine possible causes of the observed anisotropy, ideally the elastic parameters of the constituents and their contribution to the compound medium. This is possible, though under several restrictions: Not all TI media are long-wave equivalent to a periodically layered sequence of isotropic layers. Those that are can be "modeled" by a variety of layer sequences. Every TI medium that can be modeled at all can be modeled by as few as three layers, but the set of all models is a three-parametric manifold. If a TI medium can be modeled by two constituents only, this can be done only in one way, unless the constituents have the same ratio of S- to P-velocity. In that case, the set of possible models forms a one-parametric manifold.

USE OF A TORSIONAL WAVE SENSOR TO MEASURE THE LEVEL OF A COMPRESSIBLE FLUID

In nuclear pressurized water reactors, information about fluid masses or fluid levels is required, especially in the reactor vessel, where the core of the reactor must be immersed, to avoid damage or accidents. To reinforce the existing instrumentation, the possibilities of an immersed torsional wave sensor (that is, an elastic solid waveguide) have already been looked into and modelled, considering an incompressible surrounding fluid. Yet, in case of depressurization, the fluid can turn into a two-phase fluid. This is the reason why a way to extend the existing model has been investigated. As a first step, in this paper, the compressibility of the surrounding fluid has been taken into account.Some assumptions have been made: the transverse dimensions of the waveguide are small compared to its length and the wavelengths in the fluid. The focus is on a cylindrical waveguide, with an elliptic cross-section. Use is made of elliptic co-ordinates and Mathieu functions. The analysis starts with the elasticity equations for the waveguide. Then, from the exact expression of the pressure exerted by the fluid on the waveguide boundary, a long-wavelength approximation is obtained. In the end, the principle of energy conservation is applied, leading to an approximate equation governing the fluid-loaded waveguide motion. Finally, some simulations are made, highlighting the influence of the compressibility.

Scattering of a radially symmetric spin wave on a magnetic vortex in a two-dimensional easy-plane ferromagnet

The scattering amplitude for a radially symmetric spin wave (azimuthal number m=0) on a vortex in an easy-plane ferromagnet is found by analytical and numerical calculations in the long-wavelength approximation (wave number much larger than the inverse size of the vortex core). It is found that the scattering amplitude of a radially symmetric spin wave is smaller than that for a translational mode (m=±1) with the same value of the wave number.

Photodisintegration and electrodisintegration of3Heat threshold andpdradiative capture

The present work reports results for: pd radiative capture observables measured at center-of-mass (c.m.) energies in the range 0--100 keV and at 2 MeV by the TUNL and Wisconsin groups, respectively; contributions to the Gerasimov-Drell-Hearn (GDH) integral in 3He from the two- up to the three-body breakup thresholds, compared to experimental determinations by the TUNL group in this threshold region; longitudinal, transverse, and interference response functions measured in inclusive polarized electron scattering off polarized 3He at excitation energies below the threshold for breakup into ppn, compared to unpolarized longitudinal and transverse data from the Saskatoon group. The calculations are based on a realistic Hamiltonian with two- and three-nucleon interactions and a realistic current operator, including one- and two-body components. The theoretical predictions obtained by including only one-body currents are in violent disagreement with data. These differences between theory and experiment are, to a large extent, removed when two-body currents are taken into account, although some rather large discrepancies remain in the c.m. energy range 0--100 keV, particularly for the pd differential cross section and tensor analyzing power at small angles, and contributions to the GDH integral. A rather detailed analysis indicates that these discrepancies have, in large part, a common origin, and can be traced back to an excess strength obtained in the theoretical calculation of the E1 reduced matrix element associated with the pd channel having L,S,J=1,1/2,3/2. It is suggested that this lack of E1 strength observed experimentally might have implications for the nuclear interaction at very low energies. Finally, the validity of the long-wavelength approximation for electric dipole transitions is discussed.

Interaction of sound waves with an inhomogeneous magnetized plasma in a strongly nonlinear resonant slow-wave layer

The nonlinear theory of driven magnetohydrodynamic (MHD) waves in resonant slow-wave layers developed by Ruderman et al. [Phys. Plasmas4, 75 (1997)] is used to study the interaction of sound waves with a one-dimensional planar magnetic plasma configuration. The physical problem studied here is the same as that considered by Ruderman et al. [Phys. Plasmas4, 91 (1997)]. The difference is in the description of the wave motion in the resonant layer. Ruderman et al. assumed that dissipation dominates non-linearity in the resonant layer and considered the nonlinear term in the governing equation for the wave motion in the resonant layer as a perturbation. In contrast, it is assumed in the present paper that nonlinearity dominates dissipation in the resonant layer. The solution to the governing equation for the wave motion in the resonant layer is obtained in the approximation of strong nonlinearity, and it is shown that the amplitude of the wave motion saturates when the Reynolds number tends to infinity. This solution is then used to derive the nonlinear connection formula that determines the jump across the resonant layer in the velocity component in the direction of inhomogeneity. The nonlinear connection formula is, in turn, used to obtain a nonlinear one- dimensional integral equation describing the outgoing sound wave, which appears owing to partial reflection of the incoming sound wave from the inhomogeneous plasma. The solution to this integral equation is obtained in the form of a sinusoidal wave under the assumption that an incoming sound wave contains the fundamental harmonic only. The coefficient of wave-energy absorption is calculated analytically in the long-wavelength approximation and numerically for arbitrary wavelengths.

Comparison of long-wavelengthT-matrix multiple-scattering theory and size-dependent Maxwell-Garnett formula

Wave attenuation in a dielectric-in-dielectric composite is calculated using the long-wavelength T-matrix multiple-scattering theory and the size-dependent Maxwell–Garnett formula. Results obtained are first compared, and then followed by their comparisons with the experimental results and other theoretical results. An interesting observation made is that the size-dependent Maxwell–Garnett formula predicts monotonically increasing wave attenuation with increasing concentration of inclusions, whereas the computed results from the multiple-scattering theory and other formulas, together with the experimental results, indicate maximum wave attenuation at a certain concentration of inclusions. It is shown that the size-dependent Maxwell–Garnett formula gives good prediction of wave attenuation only up to inclusion concentration of about 2%, and the T-matrix multiple-scattering theory in the long-wavelength approximation gives good prediction of wave attenuation even beyond the inclusion concentration of 2%. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 23: 1–4, 1999.

Proton polarization shifts in electronic and muonic hydrogen

The contribution of virtual excitations to the energy levels of electronic and muonic hydrogen is investigated combining a model-independent approach for the main part with quark model predictions for the remaining corrections. Precise values for the polarization shifts are obtained in the long-wavelength dipole approximation by numerically integrating over measured total photoabsorption cross sections. These unretarded results are considerably reduced by including retardation effects in an approximate way since the average momentum transfer (together with the mean excitation energy) turns out to be larger than usually assumed. Transverse and seagull contributions are estimated in a simple harmonic oscillator quark model and found to be non-negligible. Possible uncertainties and improvements of the final results are discussed.

Experiments on space-charge waves in electron beams propagating through a resistive-wall channel

Localized longitudinal space-charge waves in a transport channel with a resistive wall are investigated experimentally. The space-charge waves with various pulse widths are generated in electron beams with energies of 3.0–8.5 keV and currents of 30–135 mA, and they are transported through a resistive channel with a resistance of 5–10 kΩ and a length of 1 m. The resistive channel, made of a glass tube with a resistive material coating, is surrounded by a long solenoid which provides the focusing for the beam. The localized space-charge waves are measured with current monitors and energy analyzers at the entrance and exit of the resistive channel, and the wave-amplitude growth and damping rates are determined. The measured results are compared with the theory in the long-wavelength range. For localized waves with short widths, where the long-wavelength approximation is not valid any more, dispersion and distributed capacitance effects on the growth/damping rates are discussed. In addition, preliminary results on the energy width measurements of space-charge waves are presented.

Solitons in the Two-Dimensional Antiferromagnetic Heisenberg Model**The project supported in part by National Natural Science Foundation of China

An effective Hamiltonian of the two-dimensional antiferromagnetic Heisenberg model is derived by using the Holstein–Primakoff transformation. Three nonlinear coupled partial equations of motion are obtained. In the long-wavelength approximation, these equations, are reduced to the envelope function equations by the method of multiple scales. The amplitude functions satisfy the nonlinear Schrödinger equation. Introducing an inverse scattering transformation, the single-, two- and multi-soliton solutions in the two-dimensional antiferromagnetic Heisenberg model are investigated.

Optical response of excitonic polaritons in photonic crystals

Nonlocal investigations are presented for exciton-photon coupling in photonic crystals consisting of two kinds of alternating slabs (CuCl/NaCl), for which excitons exist only in one (CuCl) of the two slabs. Studies are carried out for several typical combinations of period and slab thickness. The lower branch of the excitonic polariton for this system is found to split into many small bands separated by small band gaps (polariton gaps). This phenomenon is explained as the band splitting caused by the coherent interference of polaritonic waves in periodic systems. At the same time, the group velocity of light is greatly reduced in the presence of the excitons. The present nonlocal study demonstrates a double exciton-photon coupling, in which the upper branch of the polariton couples again with the size-quantized exciton states. A long-wavelength approximation is also presented along with a discussion of its validity for simplifying the nonlocal theory. The absorbance and reflectance spectra computed using the transfer matrices exactly reproduce the above small bands for the same systems. An examination of the coupling scheme among excitons, photons, and the structural periodicity indicates that the former two couple with each other more strongly than the other combinations of them. The exciton component of polariton, which is localized in each slab in darkness, could be construed as being delocalized with the assistance of the photon.

HAMILTON–JACOBI APPROACH TO PRE-BIG BANG COSMOLOGY AT LONG WAVELENGTHS

We apply the long-wavelength approximation to the low-energy effective string action in the context of the Hamilton–Jacobi theory. The Hamilton–Jacobi equation for the effective string action is explicitly invariant under scale factor duality. We present the leading-order, general solution of the Hamilton–Jacobi equation. The Hamilton–Jacobi approach yields a solution consistent with the Lagrange formalism. The momentum constraints take an elegant, simple form. Furthermore, this general solution reduces to the quasi-isotropic one, if the evolution of the gravitational radiation is neglected. Duality transformation for the general solution is written as a coordinate transformation in an abstract field space.

Generalized quantum hydrodynamics of a trapped dilute Bose gas

Quantal kinetic equations for particle and current densities of condensate and non-condensate in a confined Bose-condensed fluid are set up by expansion of the one-body density matrix about its diagonal. A microscopic Landau equation for superfluid flow in the inhomogeneous system is derived. Current-density functional theory in the local (long-wavelength) approximation is then used to propose a unified treatment of various damping mechanisms.

Theoretical investigations of the temperature dependence of zero-field splitting for in crystals

In this paper, we carry out a detailed theoretical investigation of the temperature dependence of zero-field splitting (characterized by of crystals by taking into account both the static contributions due to the thermal expansion of crystal and the vibrational contributions due to the electron - phonon interaction. The static contributions are calculated from the spin - orbit coupling mechanism, the relativistic mechanism, the covalency and overlap mechanism and the spin - spin interaction mechanism. Similar to the studies on the specific heat of crystals, the vibrational contribution of phonons of acoustic branches is given using the long-wavelength approximation and that of phonons of optical branches is calculated using a single-frequency model. The calculated results show that the contribution coming from the coupling with optical phonons is comparable with that due to the thermal expansion and that, to reach good fits between the theoretical and experimental , all the contributions from the thermal expansion and the electron - phonon (including the optical and acoustic phonons) interaction should be taken into account.

On Gravitational Radiation Graviton Number Density: Application to a Nambu String

A formalism is developed to compute the number density of gravitons, of specified energies, produced by an arbitrary external energy-momentum tensor source at any temperature. The formalism is applied to a simple Nambu string without making the usual assumption of a long wavelength approximation (L.W.A.). This exact result is also compared to the L.W.A.

Adhesion of metals and semiconductors analyzed by a dielectric formalism

This paper discusses a model of the adhesive interaction of metals and semiconductors, based on a dielectric formalism and using the concepts of collective excitations — plasmons of the electron-ion system. Expressions are obtained in terms of the jellium model in the longwavelength approximation for the adhesion energy and the adhesive interaction force and are determined via the dispersion dependences of the energies of surface plasma oscillations for various materials whose surfaces are separated by a gap of arbitrary magnitude. The adhesion energies and the adhesive interaction forces are calculated for a number of simple and transition metals and semiconductors, and the adhesion characteristics are also obtained for the contact of the given materials with an insulating medium.

Effect of the Electric Field on Wave Motion in a Thin Suspension Layer Flowing Over an Inclined Plane

Stability of surface gravity waves in an inclined layer of rheological fluid in the presence of an arbitrarily oriented electric field is considered to investigate the effect of electric fields on wave stability. Rheological equations used for a dilute suspension of the rigid dielectric ellipsoids take into account the influence of electric fields on a particular orientation. The evolution equation is derived as a long-wavelength approximation which includes a set of nondimensional parameters responsible for the behaviour of the suspension. Solution of the evolution equation is obtained in the form of a nonlinear wave with the amplitude and phase slowly varying in time in such a way as to allow determination of the curves of neutral stability, bifurcations, suband supercritical instabilities. The results of calculations show that the electric field can both stabilise or destabilise waves.

Theoretical studies of the temperature dependence of zero-field splitting of Cr3+ centers in ruby.

Detailed theoretical studies of the temperature dependence of the zero-field splitting [characterized by \ensuremath{\Delta}D(T)=D(T)-D(0) or dD/dT] of ruby have been made by taking into account both the static contribution due to the thermal expansion of the lattice and the vibrational contribution due to the electron-phonon interaction. The static part is calculated by using the local thermal expansion coefficients ${\mathrm{\ensuremath{\alpha}}}_{\mathit{i}}$ in the vicinity of the ${\mathrm{Cr}}^{3+}$ ions, which are obtained from the local compressibilities ${\mathrm{\ensuremath{\sigma}}}_{\mathit{i}}$ and the well-known relation ${\mathrm{\ensuremath{\alpha}}}_{\mathit{i}}$=${\mathit{C}}_{\mathit{v}}$\ensuremath{\gamma}${\mathrm{\ensuremath{\sigma}}}_{\mathit{i}}$/V. The vibrational part includes the contributions from the acoustic and optical phonons. As in specific-heat studies of crystals, the vibrational contribution of phonons of the acoustic branches is calculated using the long-wavelength approximation, and that of phonons of the optical branches is calculated using a single-frequency model. The calculated results show that, to explain satisfactorily the temperature dependence of the zero-field splitting (ZFS), all of the contributions from the thermal expansion and the electron-phonon interaction should be considered. The static contribution is due mainly to the variations of bond angles as the temperature changes, which results in the static part of the temperature dependence of ZFS being opposite in sign to the observed temperature dependence. Thus the contribution due to the thermal expansion cannot be regarded as the main one. Among the various contributions, the contribution of acoustic phonons is the greatest in magnitude, and it has the same sign as the observed value. The contribution of optical phonons is the smallest and yet cannot be ignored. \textcopyright{}1996 The American Physical Society.

Analytical results for a hole in an antiferromagnet.

The Green's function for a hole moving in an antiferromagnet is derived analytically in the long-wavelength limit. We find that the infrared divergence is eliminated in two and higher dimensions so that the quasiparticle weight is finite. Our results also suggest that the hole motion is polaronic in nature with a bandwidth proportional to $t/J \exp [-c (t/J)^2] $ ($c$ is a constant). The connection of the long-wavelength approximation to the first-order approximation in the cumulant expansion is also clarified.

Gravitational Wave Interaction with Normal and Superconducting Circuits

The interaction, in the long-wavelength approximation, of normal and superconducting electromagnetic circuits with gravitational waves is investigated. We show that such interaction takes place by modifying the physical parameters R, L, C of the electromagnetic devices. Exploiting this peculiarity of the gravitational field we find that a circuit with two plane and statically charged condensers set at right angles can be of interest as a detector of periodic gravitational waves.