General Wave Vector Research Articles

Electromagnetic wave propagation in general Kasner-like metrics

The curved spacetime Maxwell equations are applied to the anisotropically expanding Kasner metrics. Using the application of vector identities we derive second-order differential wave equations for the electromagnetic field components; through this explicit derivation, we find that the second-order wave equations are not uncoupled for the various components (as previously assumed), but that gravitationally induced coupling between the electric and magnetic field components is generated directly by the anisotropy of the expansion. The lack of such coupling terms in the wave equations from several prior studies may indicate a generally incomplete understanding of the evolution of electromagnetic energy in anisotropic cosmologies. Uncoupling the field components requires the derivation of a fourth-order wave equation, which we obtain for Kasner-like metrics with generalized expansion/contraction rate indices. For the axisymmetric Kasner case, [Formula: see text], we obtain exact field solutions (for general propagation wave vectors), half of which appear not to have been found before in previous studies. For the other axisymmetric Kasner case, [Formula: see text], we use numerical methods to demonstrate the explicit violation of the geometric optics approximation at early times, showing the physical phase velocity of the wave to be inhibited towards the initial singularity, with [Formula: see text] as [Formula: see text].

Langevin simulations of the half-filled cubic Holstein model

Over the past several years, reliable Quantum Monte Carlo results for the charge density wave transition temperature $T_{cdw}$ of the half-filled two dimensional Holstein model in square and honeycomb lattices have become available for the first time. Exploiting the further development of numerical methodology, here we present results in three dimensions, which are made possible through the use of Langevin evolution of the quantum phonon degrees of freedom. In addition to determining $T_{cdw}$ from the scaling of the charge correlations, we also examine the nature of charge order at general wave vectors for different temperatures, couplings, and phonon frequencies, and the behavior of the spectral function and specific heat.

Momentum-Space Geometric Structure of Helical Evanescent Waves and Its Implications on Near-Field Directionality

In this paper, a momentum-space geometrical structure in helical evanescent electromagnetic waves is revealed. It is shown that for every helical evanescent wave on a helicity-dependent half tangent line in momentum space, the orientation of each of its field, spin, and Poynting vectors is the same. This geometric structure is revealed in a remarkable relation between the far-field and near-field components of the angular spectrum. Any general evanescent wave vector is linked to two points on the ${k}_{\ensuremath{\rho}}={k}_{0}$ circle of propagating wave vectors via two helicity-dependent tangent lines. Knowing the field of a general dipolar source on the ${k}_{\ensuremath{\rho}}={k}_{0}$ circle is sufficient to determine its entire evanescent angular spectrum. By applying this concept, we gain insights into near-field directionality by showing that every zero in the angular spectrum is a helicity singularity where two half tangent lines of opposite helicity intersect. A powerful method for the synthetic design of near-field directional sources is also devised, using structured helical illumination to gain full control of the near-field directionality. The results provide fundamental insight into helical evanescent waves and have implications in areas where chiral light-matter interaction plays a central role.

Conduction band population in graphene in ultrashort strong laser field: Case of massive Dirac particles

The Dirac-like quasiparticles in honeycomb graphene lattice are taken to possess a non-zero effective mass. The charge carriers involve to interact with a femtosecond strong laser pulse. Due to the scattering time of electrons in graphene ([Formula: see text]10–100 fs), the one femtosecond optical pulse is used to establish the coherence effect and, consequently, it can be realized to use the time-dependent Schrödinger equation for electron coupled with strong electromagnetic field. Generalized wave vector of relativistic electrons interacting with electric field of laser pulse causes to obtain a time-dependent electric dipole matrix element. Using the coupled differential equations of a two-state system of graphene, the density of probability of population transition between valence (VB) and conduction bands (CB) of gapped graphene is calculated. In particular, the effect of bandgap energy on dipole matrix elements at the Dirac points and resulting CB population (CBP) is investigated. The irreversible electron dynamics is achieved when the optical pulse end. Increasing the energy gap of graphene results in decreasing the maximum CBP.

Theory of anharmonic phonons in two-dimensional crystals

Anharmonic effects in an atomic monolayer thin crystal with honeycomb lattice structure are investigated by analytical and numerical lattice dynamical methods. Starting from a semi-empirical model for anharmonic couplings of third and fourth order, we study the in-plane and out-of-plane (flexural) mode components of the generalized wave vector dependent Gr\"uneisen parameters, the thermal tension and the thermal expansion coefficients as function of temperature and crystal size. From the resonances of the displacement-displacement correlation functions we obtain the renormalization and decay rate of in-plane and flexural phonons as function of temperature, wave vector and crystal size in the classical and in the quantum regime. Quantitative results are presented for graphene. There we find that the transition temperature from negative to positive thermal expansion is lowered with smaller system size and by renormalization of the flexural mode frequency. Extensive numerical analysis throughout the Brillouin zone explores various decay and scattering channels. The relative importance of Normal and Umklapp processes is investigated. The work is complementary to crystalline membrane theory and computational studies of anharmonic effects in two-dimensional crystals.

The Jeans Equation Generalization for the Rotating Universe

The generalization of Jeans equation in expanding and rotating Universe is given. We found the generalized frequency of baryonic substrate oscillations in the rotating Universe. In doing this, two cases were considered: the generalized wave vector coincides with the Jeans wave vector and second case, when the generalized wave vector tends to zero.

Band gap properties of two-dimensional photonic crystals with rhombic lattice

A new structure of two-dimensional photonic crystals (PCs) with rhombic lattice is proposed in this paper. It provides more flexibility in the design of photonic crystal devices and makes the designer be able to choose a more suitable lattice angle to satisfy different demands. The first Brillouin zone (1st BZ) of this structure is discussed and the general wave vectors are derived. The plane wave expansion (PWE) method is used to analyze the band gap properties. The impact of different lattice angels on the band gaps is analyzed, and the band gap map is also given.

Hamiltonian formulation of nonlinear spin-wave dynamics: Theory and applications

A systematic step-by-step development of nonlinear spin-wave theory within the framework of a Hamiltonian formalism is given. The expansion coefficients in the spin-wave Hamiltonian up to the fourth order in the canonical spin-wave amplitudes for a uniformly magnetized ellipsoidal sample are given in general form. This is done for a general orientation of the external field and for a general wave vector. Applications are given for (A) the second-order Suhl spin-wave instability coupling coefficients, (B) the spin-wave wave-vector-dependent nonlinear frequency shift for an in-plane magnetized thin film, and (C) the uniform magnetization mode (ferromagnetic resonance) nonlinear frequency shift for an obliquely magnetized thin film. The analytical results for (C) are compared with results obtained from a time forward numerical analysis of the torque equation of motion and show a near-perfect match.

Research on Three Types of Rhombus Lattice Photonic Band Structures

The gap-midgap ratio for three types of rhombus lattice photonic band structures are analyzed by plane wave expansion method, which is confirmed by the HFSS simulation. Firstly, general wave vectors in the first Briliouin zone are derived. Secondly, the gap-midgap ratios as a function of filling factor and background material are investigated, respectively. These results would provide theoretical instruction for designing arbitrary bend waveguides or other optical integrated devices using photonic crystal with a rhombus lattice.

二维菱形晶格光子带隙研究

The relative band gap for a rhombus lattice photonic crystal is studied by plane wave expansion method and high frequency structure simulator (HFSS) simulation. General wave vectors in the first Briliouin zone are derived. The relative band gap as a function of air-filling factor and background material is investigated, respectively, and the nature of photonic band gap for different lattice angles is analyzed by the distribution of electric energy. These results would provide theoretical instruction for designing optical integrated devices using photonic crystal with a rhombus lattice.

Invariant Form of Multipolar Interactions and Relation between Antiferro-Quadrupolar Order and Field-Induced Magnetic Moments

The invariant interaction form between multipoles, including the octupoles, is studied for three types of cubic lattices: s.c., b.c.c. and f.c.c. The coupling terms can be arranged in a form similar to the hopping matrices between LCAO's. By using it, order parameters in the magnetic field are classified into groups in which they couple with each other, and the symmetry of the antiferro-quadrupolar (AFQ) moment is analyzed through induced antiferromagnetic moments (AFM). In this way the table for s.c. by Shiina et al. [J. Phys. Soc. Jpn. 66 (1997) 1741] is generalized for general wave vectors of the three lattice types. Recent experimental results of TmTe having the f.c.c. structure are analyzed from this viewpoint. The nature of the ferromagnetic moment below the AFM transition in the AFQ phase is also discussed. Finally brief comments are given also on field-induced moments in PrFe 4 P 12 and NpO 2 .

Spin-wave spectrum of a two-dimensional itinerant electron system: Analytic results for the incommensurate spiral phase in the strong-coupling limit

We study the zero-temperature spin fluctuations of a two-dimensional itinerant-electron system with an incommensurate magnetic ground state described by a single-band Hubbard Hamiltonian. We introduce the (broken-symmetry) magnetic phase at the mean-field (Hartree-Fock) level through a \emph{spiral spin configuration} with characteristic wave vector $\gmathbf{Q}$ different in general from the antiferromagnetic wave vector $\gmathbf{Q_{AF}}$, and consider spin fluctuations over and above it within the electronic random-phase (RPA) approximation. We obtain a \emph{closed} system of equations for the generalized wave vector and frequency dependent susceptibilities, which are equivalent to the ones reported recently by Brenig. We obtain, in addition, analytic results for the spin-wave dispersion relation in the strong-coupling limit of the Hubbard Hamiltonian and find that at finite doping the spin-wave dispersion relation has a \emph{hybrid form} between that associated with the (localized) Heisenberg model and that associated with the (long-range) RKKY exchange interaction. We also find an instability of the spin-wave spectrum in a finite region about the center of the Brillouin zone, which signals a physical instability toward a different spin- or, possibly, charge-ordered phase, as, for example, the stripe structures observed in the high-Tc materials. We expect, however, on physical grounds that for wave vectors external to this region the spin-wave spectrum that we have determined should survive consideration of more sophisticated mean-field solutions.

Theory of magnetic excitations of spin-pair system KCuCl 3

A general expression for the dispersion of magnetic excitations of KCuCl 3-type spin-pair systems is derived on the basis of the pair mean-field approximation. The magnetic excitations of KCuCl 3 observed by inelastic neutron scattering are well reproduced, and it is predicted that two modes can be observable for general wave vectors.

Theory of temperature-dependent angle-resolved-photoemission spectrum of heavy-fermion semiconductors

The heavy-fermion semiconductors are a class of strongly correlated materials, that at high temperatures show properties similar to those of heavy-fermion materials, but at low temperatures show a crossover into a semiconducting state. The low-temperature insulating state is characterized by an anomalously small energy gap, varying between 10 and 100 K. The smallness of the gap is attributed to the result of a many-body renormalization. We calculate the temperature dependence of the electronic spectral density of states, using the Anderson lattice model at half-filling, together with a 1/N expansion, where N is the degeneracy of the f orbitals. The spectrum is calculated to second order in 1/N using a slave boson technique. We find that to first order the system is an indirect gap semiconductor, with a temperature-dependent renormalized band structure. The indirect gap is subject to a temperature-dependent many-body renormalization, and leads to a temperaturedependent sharp structure in the angle-integrated spectrum at the indirect threshold. To second order in 1/ N, one has to include charge fluctuations that are represented by fluctuations in the slave boson field. The effect of emission and absorption of fluctuations in the slave boson field is to broaden the angle-resolved spectrum A(k,v), yielding a low-energy tail to the spectrum that, for general wave vectors k, extends all the way down to the indirect threshold. We show that as the temperature is reduced, the structure in the vicinity of the Fermi energy sharpens up. We apply the theory to experiments on the materials FeSi and Ce3Bi4Pt3. @S0163-1829~98!03948-4#

Effect of hot pressing on the modulated structure of Zr0.98Sn0.02TiO4

Abstract With the use of X-ray diffraction and neutron scattering, the effect of hot pressing on the modulated structure in Zr0.98Sn0.02TiO4 was investigated in order to obtain information concerning the nature of the competing forces that bring about a structural instability at a general wave-vector. It was found that an increase in pressure lowers the normal-to-incommensurate and incommensurate-to-commensurate transitions (dT i/dP i ≈ −7.1K kbar−1 and dT c/dP c ≈ −8.8 K kbar−1 respectively). The latter transition displays a distinct hysteresis.

A thermodynamic basis for charged particles transport in viscoelastic fluids

A calculation for the generalized longitudinal stress modulus and electric conductivity in an ionic-viscoelastic medium is presented. The system is described within the framework of extended irreversible thermodynamics in terms of the regular conserved variables and of an additional set of independent variables consisting of the stress tensor, its trace, and the electric flux. Using the standard procedure, we derive the time evolution equations for the additional variables. These equations are used to obtain general wave vector and frequency dependent expressions for measurable properties of the system. We obtain for the linear case results that have not been derived previously in the literature.

Effect of electric field on the phase transition in ZrTiO4 ceramic

An x-ray study of electric fields on the incommensurate phase transition in ZrTiO4 ceramic was performed in order to obtain information concerning the nature of the competing forces that give rise to structural instability at a general wave vector. It was found that an increase in dc electric field increases the normal incommensurate phase transition temperature [(dTi/dEi)≅+1.7 °C cm/kV]. The electric field dependence of the incommensurate to commensurate transition was also investigated [(dTc/dEc)≅+1.5 °C cm/kV].

Effect of pressure and electric field on the phase transition in zirconium titanate

An X-ray study of the effect of pressure and electric field on the incommensurate phase transition in ZrTiO 4 was performed in order to obtain the information concerning the nature of the competing forces that give rise to a structural instability at a general wave-vector. It was found not only that an increase in pressure lowers the transition temperature ( dT i dP i ≅ −6.9 K kbar −1 ), but also that an increase in d.c. electric field shifts the transition temperature ( dT i dE i ≅ +1.7 deg cm kV −1 ) to a higher. The pressure and electric field dependence of the incommensurate to commensurate transition were also investigated ( dT c dP c ≅ −9.0 K kbar −1 ) and ( dT c dE c ≅ +1.5 deg cm kV −1 ), respectively.

Zero-temperature spin-wave spectrum of the critical two-layer S=1/2 antiferromagnet.

Series expansions about the interlayer dimer limit are calculated to eighth order in the intralayer coupling for the T=0 antiferromagnetic susceptibility and elementary excitation spectrum of the two-layer, S=1/2, square lattice Heisenberg antiferromagnet. Extrapolations of the susceptibility and the gap series yield an estimate of the critical interlayer/intralayer coupling ratio ${\mathit{J}}_{2}$/${\mathit{J}}_{1}$=2.54\ifmmode\pm\else\textpm\fi{}0.02, in agreement with several previous numerical calculations. The spin-wave velocity at criticality is determined by an analysis of the excitation spectrum series: the result, \ensuremath{\Elzxh}c/${\mathit{J}}_{1}$a=1.89\ifmmode\pm\else\textpm\fi{}0.02, is very precise and consistent with other estimates based on numerical calculations at finite temperature. The critical spin-wave dispersion at general wave vectors is shown to deviate significantly from a uniformly renormalized mean-field spectrum. \textcopyright{} 1996 The American Physical Society.

Low-energy properties of fermions with singular interactions.

We calculate the fermion Green function and particle-hole susceptibilities for a degenerate two-dimensional fermion system with a singular gauge interaction. We show that this is a strong-coupling problem, with no small parameter other than the fermion spin degeneracy N. We consider two interactions, one arising in the context of the t-J model and the other in the theory of half-filled Landau level. For the fermion self-energy we show that the qualitative behavior found in the leading order of perturbation theory is preserved to all orders in the interaction. The susceptibility ${\mathrm{\ensuremath{\chi}}}_{\mathit{Q}}$ at a general wave vector Q\ensuremath{\ne}2${\mathbf{p}}_{\mathbf{F}}$ retains the Fermi-liquid form. However, the 2${\mathit{p}}_{\mathit{F}}$ susceptibility ${\mathrm{\ensuremath{\chi}}}_{2\mathit{p}\mathit{F}}$ either diverges as T\ensuremath{\rightarrow}0 or remains finite but with nonanalytic wave-vector, frequency, and temperature dependence. We express our results in the language of recently discussed scaling theories, give the fixed-point action, and show that at this fixed point the fermion-gauge-field interaction is marginal in d=2, but irrelevant at low energies in d\ensuremath{\ge}2.