Zero-frequency Limit Research Articles

Low-frequency absorption cross section of the electromagnetic waves for extreme Reissner-Nordström black holes in higher dimensions

We investigate the low-frequency absorption cross section of the electromagnetic waves for the extreme Reissner-Nordstrom black holes in higher dimensions. We first construct the exact solutions to the relevant wave equations in the zero-frequency limit. In most cases it is possible to use these solutions to find the transmission coefficients of partial waves in the low-frequency limit. We use these transmission coefficients to calculate the low-frequency absorption cross section in five and six spacetime dimensions. We find that this cross section is dominated by the modes with l=2 in the spherical-harmonic expansion rather than those with l=1, as might have been expected, because of the mixing between the electromagnetic and gravitational waves. We also find an upper limit for the low-frequency absorption cross section in dimensions higher than six.

Density-operator approaches to transport through interacting quantum dots: Simplifications in fourth-order perturbation theory

Various theoretical methods address transport effects in quantum dots beyond single-electron tunneling while accounting for the strong interactions in such systems. In this paper we report a detailed comparison between three prominent approaches to quantum transport: the fourth-order Bloch-Redfield quantum master equation (BR), the real-time diagrammatic technique (RT), and the scattering rate approach based on the T-matrix (TM). Central to the BR and RT is the generalized master equation for the reduced density matrix. We demonstrate the exact equivalence of these two techniques. By accounting for coherences (nondiagonal elements of the density matrix) between nonsecular states, we show how contributions to the transport kernels can be grouped in a physically meaningful way. This not only significantly reduces the numerical cost of evaluating the kernels but also yields expressions similar to those obtained in the TM approach, allowing for a detailed comparison. However, in the TM approach an ad hoc regularization procedure is required to cure spurious divergences in the expressions for the transition rates in the stationary (zero-frequency) limit. We show that these problems derive from incomplete cancellation of reducible contributions and do not occur in the BR and RT techniques, resulting in well-behaved expressions in the latter two cases. Additionally, we show that a standard regularization procedure of the TM rates employed in the literature does not correctly reproduce the BR and RT expressions. All the results apply to general quantum dot models and we present explicit rules for the simplified calculation of the zero-frequency kernels. Although we focus on fourth-order perturbation theory only, the results and implications generalize to higher orders. We illustrate our findings for the single impurity Anderson model with finite Coulomb interaction in a magnetic field.

Investigation of the Linear and Nonlinear Optical Susceptibilities of KTiOPO4 Single Crystals: Theory and Experiment

Experimental and theoretical studies of the linear and nonlinear optical susceptibilities for single crystals of potassium titanyl phosphate KTiOPO₄ are reported. The state-of-the-art full potential linear augmented plane wave method, based on the density functional theory, was applied for the theoretical investigation. The calculated direct energy band gap at Γ, using the Engel-Vosko exchange correlation functional, is found to be 3.1 eV. This is in excellent agreement with the band gap obtained from the experimental optical absorption spectra (3.2 eV). We have calculated the complex dielectric susceptibility ε(ω)dispersion, its zero-frequency limit ε₁(0) and the birefringence of KTiOPO₄. The calculated birefringence at the zero-frequency limit Δn(0) is equal to about 0.07 and Δn(ω) at 1.165 eV (λ = 1064 nm) is 0.074. We also report calculations of the complex second-order optical susceptibility dispersions for the principal tensor components: χ₁₁₃((2))(ω), χ₂₃₂((2))(ω), χ₃₁₁((2))(ω), χ₃₂₂((2))(ω), and χ₃₃₃((2))(ω). The intra- and interband contributions to these susceptibilities are evaluated. The calculated total second order susceptibility tensor components |χ(ijk)((2))(ω)| at λ = 1064 nm for all the five tensor components are compared with those obtained from our measurements performed by nanosecond Nd:YAG laser at the fundamental wavelength (λ = 1064 nm). Our calculations show reasonably good agreement with our experimental nonlinear optical data and the results obtained by other authors. The calculated the microscopic second order hyperpolarizability, β₃₃₃, vector component along the dipole moment direction for the dominant component χ₃₃₃((2))(ω) is found to be 31.6 × 10⁻³⁰ esu, at λ = 1064 nm.

Ab initio study of structural, elastic, electronic and optical properties of spinel SnMg 2O 4

Ab initio study of structural, elastic, electronic and optical properties of the cubic spinel oxide SnMg 2O 4 has been reported using the pseudo-potential plane-wave method within the local density approximation and the gradient generalized approximation for the exchange and correlation potential. Computed lattice constant and internal free parameters are in good agreement with the available experimental results. The elastic constants and their pressure dependence are predicted using the static finite strain technique. A linear pressure dependence of the elastic stiffnesses is found. A set of isotropic elastic parameters and related properties, namely bulk and shear moduli, Young’s modulus, Poisson’s ratio, Lamé’s coefficients, average sound velocity and Debye temperature are numerically estimated in the frame-work of the Voigt–Reuss–Hill approximation for SnMg 2O 4 polycrystalline. Band structure shows that SnMg 2O 4 has a direct band gap ( Г– Г), which increases with increase in pressure. Density of states and Mulliken population analysis show that the Mg–O bond is typically covalent due to the O-2p and Mg-2p states hybridizations. In order to understand the optical properties of SnMg 2O 4, the dielectric function, optical reflectivity, refractive index, extinction coefficient and electron energy loss function are calculated for radiation up to 40 eV. The pressure dependence of the zero-frequency limit of the real part of the dielectric function ε 1(0) and of the refractive index n(0) has been investigated. This is the first quantitative theoretical prediction of the elastic, electronic and optical properties of the SnMg 2O 4 compound, and it still awaits experimental confirmation.

Greybody factors for topological massless black holes

We study the greybody factors, the reflection and transmission coefficients for a non-minimally coupled massive scalar field in a d-dimensional topological massless black hole background in the zero-frequency limit. We show that there is a range of modes contributing to the absorption cross section, contrary to the current results where the only contribution comes from the mode with lowest angular momentum.

Semianalytical estimates of scattering thresholds and gravitational radiation in ultrarelativistic black hole encounters

Ultrarelativistic collisions of black holes are ideal gedanken experiments to study the nonlinearities of general relativity. In this paper we use semianalytical tools to better understand the nature of these collisions and the emitted gravitational radiation. We explain many features of the energy spectra extracted from numerical relativity simulations using two complementary semianalytical calculations. In the first calculation we estimate the radiation by a ``zero-frequency limit'' analysis of the collision of two point particles with finite impact parameter. In the second calculation we replace one of the black holes by a point particle plunging with arbitrary energy and impact parameter into a Schwarzschild black hole, and we explore the multipolar structure of the radiation paying particular attention to the near-critical regime. We also use a geodesic analogy to provide qualitative estimates of the dependence of the scattering threshold on the black hole spin and on the dimensionality of the spacetime.

Hysteresis in random-fieldXYand Heisenberg models: Mean-field theory and simulations at zero temperature

We examine zero-temperature hysteresis in random-field XY and Heisenberg models in the zero-frequency limit of a cyclic driving field. Exact expressions for hysteresis loops are obtained in the mean-field approximation. These show rather unusual features. We also perform simulations of the two models on a simple-cubic lattice and compare them with the predictions of the mean-field theory.

Vertex corrections for impurity scattering at a ferromagnetic quantum critical point

We study the renormalization of a non-magnetic impurity's scattering potential due to the presence of a massless collective spin mode at a ferromagnetic quantum critical point. To this end, we compute the lowest order vertex corrections in two- and three-dimensional systems, for arbitrary scattering angle and frequency of the scattered fermions, as well as band curvature. We show that only for backward scattering in D=2 does the lowest order vertex correction diverge logarithmically in the zero frequency limit. In all other cases, the vertex corrections approach a finite (albeit possibly large) value in the zero frequency limit. We demonstrate that vertex corrections are strongly suppressed with increasing curvature of the fermionic bands. Moreover, we show how the frequency dependence of vertex corrections varies with the scattering angle. We also discuss the form of higher order ladder vertex corrections and show that they can be classified according to the zero-frequency limit of the lowest order vertex correction. We show that even in those cases where the latter is finite, summing up an infinite series of ladder vertex diagrams can lead to a strong enhancement (or divergence) of the impurity's scattering potential. Finally, we suggest that the combined frequency and angular dependence of vertex corrections might be experimentally observable via a combination of frequency dependent and local measurements, such as scanning tunneling spectroscopy on ordered impurity structures, or measurements of the frequency dependent optical conductivity.

Transport coefficients, membrane couplings and universality at extremality

We present an efficient method for computing the zero frequency limit of transport coefficients in strongly coupled field theories described holographically by higher derivative gravity theories. Hydrodynamic parameters such as shear viscosity and conductivity can be obtained by computing residues of poles of the off-shell lagrangian density. We clarify in which sense these coefficients can be thought of as effective couplings at the horizon, and present analytic, Wald-like formulae for the shear viscosity and conductivity in a large class of general higher derivative lagrangians. We show how to apply our methods to systems at zero temperature but finite chemical potential. Our results imply that such theories satisfy $\eta/s=1/4\pi$ universally in the Einstein-Maxwell sector. Likewise, the zero frequency limit of the real part of the conductivity for such systems is shown to be universally zero, and we conjecture that higher derivative corrections in this sector do not modify this result to all orders in perturbation theory.

Ab-initio study of the structural, linear and nonlinear optical properties of CdAl 2Se 4 defect-chalcopyrite

The complex density functional theory (DFT) calculations of structural, electronic, linear and nonlinear optical properties for the defect chalcopyrite CdAl 2Se 4 compound have been reported using the full potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2k code. We employed the Wu and Cohen generalized gradient approximation (GGA-WC), which is based on exchange–correlation energy optimization to calculate the total energy. Also we have used the Engel–Vosko GGA formalism, which optimizes the corresponding potential for band structure, density of states and the spectral features of the linear and nonlinear optical properties. This compound has a wide direct energy band gap of about 2.927 eV with both the valence band maximum and conduction band minimum located at the center of the Brillouin zone. The ground state quantities such as lattice parameters ( a, c, x, y and z), bulk modulus B and its pressure derivative B′ are evaluated. We have calculated the frequency-dependent complex ε ( ω ) , its zero-frequency limit ε 1 ( 0 ) , refractive index n ( ω ) , birefringence Δ n ( ω ) , the reflectivity R ( ω ) and electron energy loss function L ( ω ) . Calculations are reported for the frequency-dependent complex second-order nonlinear optical susceptibilities. We find opposite signs of the contributions of the 2 ω and 1 ω inter/intra-band to the imaginary part for the dominant component through the wide optical frequency range.

First-principles study of the electronic and optical properties of rutile TiO2

Abstract The electronic, structural properties and optical properties of the rutile TiO2 have been reported using the full potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2K code. We employed the generalized gradient approximation (GGA), which is based on exchange-correlation energy optimization to calculate the total energy. Also we have used the Engel–Vosko GGA formalism, which optimizes the corresponding potential for band structure calculations. Our results including lattice parameter, bulk modulus, density of states, the reflectivity spectra, the refractive index and band gap are compared with the experimental data. We present calculations of the frequency-dependent complex dielectric function e ( ω ) and its zero-frequency limit e 1 ( 0 ) .

On the computation and contribution of conductivity in molecular ionic liquids

In this study we present the results of the molecular dynamics simulation of the ionic liquids: 1-butyl-3-methyl-imidazolium tetrafluoroborate and trifluoromethylacetate as well as 1-ethyl-3-methyl-imidazolium dicyanamide. Ionic liquids are characterized by both a molecular dipole moment and a net charge. Thus, in contrast to a solution of simple ions in a (non-) polar solvent, rotational and translational effects influence the very same molecule. This study works out the theoretical framework necessary to compute the conductivity spectrum and its low frequency limit of ionic liquids. Merging these computed conductivity spectra with previous simulation results on the dielectric spectra of ionic liquids yields the spectrum of the generalized dielectric constant, which may be compared to experiments. This spectrum was calculated for the three ionic liquids over six orders of magnitude in frequency ranging from 10 MHz to 50 THz. The role of rotation and translation and their coupling term on the generalized dielectric constant is discussed in detail with a special emphasis on the zero-frequency limit. Thereby, the frequency dependence of the cross correlation between the collective rotational dipole moment and the current is discussed.

Optical properties of the alkaline-earth fluorohalides matlockite-type structure SrFX (X=Cl, Br, I) compounds

The optical properties of the SrFX (X=Cl, Br, I) compound have been reported using the full potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2K code. We employed the generalized gradient approximation (GGA), which is based on exchange-correlation energy optimization to calculate the total energy. Also we have used the Engel–Vosko GGA formalism, which optimizes the corresponding potential for band structure calculations. Our calculations show that the valence band maximum (VBM) and conduction band minimum (CBM) are located at Γ resulting in a direct energy gap. We present calculations of the frequency-dependent complex dielectric function ε ( ω ) and its zero-frequency limit ε 1 (0). We find that the value of ε 1 (0) increases on decreasing the energy gap. The reflectivity spectra and absorption coefficient have been calculated and compared with the available experimental data.

Optical properties of alkaline-earth fluorohalides BaFX (X = Cl, Br, I) compounds

The ab initio calculations of the optical properties for the alkaline-earth fluorohalides BaFX (X = Cl, Br, I) compounds in its matlockite-type structure have been reported here by using the full potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2K code. We employed generalized gradient approximation (GGA), which is based on exchange–correlation energy optimization to calculate the total energy. Also we have used the Engel–Vosko GGA formalism, which optimizes the corresponding potential for band structure calculations. Our calculations show that these compounds have a direct energy band gap (Γ–Γ). We have calculated the frequency-dependent complex dielectric function ε( ω) and its zero-frequency limit ε 1(0). We find that the values of ε 1(0) increases with decreasing the energy gap. The reflectivity spectra and absorption coefficient have been calculated and compared with the available experimental data. The optical properties are analyzed and the origin of some of the peaks in the spectra is discussed in terms of the calculated electronic structure. A considerable anisotropy is found between the parallel and perpendicular components of the frequency-dependent optical properties.

Specific features in the band structure and linear and nonlinear optical susceptibilities ofLa2CaB10O19crystals

The electronic and optical properties have been calculated for monoclinic ${\mathrm{La}}_{2}\mathrm{Ca}{\mathrm{B}}_{10}{\mathrm{O}}_{19}$ (LCB) crystal using the state-of-the-art full potential linear augmented plane wave method. We present results for the band structure, density of states, birefringence, imaginary and real parts of the frequency dependent linear and nonlinear optical response. We have found that LCB is a semiconductor with an indirect energy band gap of about $4.45\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. A simple scissor operator is applied to adjust the band energy gap from the calculations to match the experimental value $(5.4\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$. The calculated birefringence of the LCB crystal has positive sign in agreement with the experimental data. Calculations are reported for the frequency-dependent complex second-order nonlinear optical susceptibilities ${\ensuremath{\chi}}_{abc}^{(2)}(\ensuremath{\omega})$ up to $6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and for zero-frequency limit ${\ensuremath{\chi}}^{2}(0)$. LCB exhibits second harmonic generation efficiency about two times larger than KDP crystal $(\mathrm{K}{\mathrm{H}}_{2}\mathrm{P}{\mathrm{O}}_{4})$.

Spin-current shot noise in mesoscopic conductors

In this paper, we present a method to investigate the spin-current shot noise in mesoscopic conductors by using scattering matrix theory and Green’s function technique. We first derive a general expression for the spin-current noise in the zero-frequency limit and extract the shot-noise component by considering the zero-temperature limit. The expression indicates that the spin-current shot noise in one lead is caused by the transmissions to the spin-resolved states in this lead and the interferences of these transmissions. As an application, we simulate the spin-current shot noise in a spin transistor and discuss its dependence on the device parameters and the bias voltages applied to the transistor. The knowledge we gain from this study will help researchers to evaluate the spin-current shot noise in future spintronic devices.

Vertical propagation of low-frequency waves in finely layered media

Multiple scattering in finely layered sediments is important for interpreting stratigraphic data, matching well-log data with seismic data, and seismic modeling. Two methods have been used to treat this problem in seismic applications: the O’Doherty-Anstey approximation and Backus averaging. The O’Doherty-Anstey approximation describes the stratigraphic-filtering effects, while Backus averaging defines the elastic properties for an effective medium from the stack of the layers. It is very important to know when the layered medium can be considered as an effective medium. In this paper, we only investigate vertical propagation. Therefore, no anisotropy effect is taken into consideration. Using the matrix-propagator method, we derive equations for transmission and reflection responses from the stack of horizontal layers. From the transmission response, we compute the phase velocity and compare the zero-frequency limit with the effective-medium velocity from Backus averaging. We also investigate how the transition from time-average medium to effective medium depends on contrast; i.e., strength of the reflection-coefficient series. Using numerical examples, we show that a transition zone exists between the effective medium (low-frequency limit) and the time-average medium (high-frequency limit), and that the width of this zone depends on the strength of the reflection-coefficient series.

Dielectric response of a polar fluid trapped in a spherical nanocavity

We present extensive molecular dynamics simulation results for the structure and the static and dynamical responses of a droplet of 1000 soft spheres carrying extended dipoles and confined to spherical cavities of radii R=2.5, 3, and 4 nm embedded in a dielectric continuum of permittivity epsilon(')>or=1. The polarization of the external medium by the charge distribution inside the cavity is accounted for by appropriate image charges. We focus on the influence of the external permittivity epsilon(') on the static and dynamic properties of the confined fluid. The density profile and local orientational order parameter of the dipoles turn out to be remarkably insensitive to epsilon('). Permittivity profiles epsilon(r) inside the spherical cavity are calculated from a generalized Kirkwood formula. These profiles oscillate in phase with the density profiles and go to a "bulk" value epsilon(b) away from the confining surface; epsilon(b) is only weakly dependent on epsilon('), except for epsilon(')=1 (vacuum), and is strongly reduced compared to the permittivity of a uniform (bulk) fluid under comparable thermodynamic conditions. The dynamic relaxation of the total dipole moment of the sample is found to be strongly dependent on epsilon(') and to exhibit oscillatory behavior when epsilon(')=1; the relaxation is an order of magnitude faster than in the bulk. The complex frequency-dependent permittivity epsilon(omega) is sensitive to epsilon(') at low frequencies, and the zero-frequency limit epsilon(omega=0) is systematically lower than the bulk value epsilon(b) of the static permittivity.

Statistical study of the conductance and shot noise in open quantum-chaotic cavities: Contribution from whispering gallery modes

In the past, a maximum-entropy model was introduced and applied to the study of statistical scattering by chaotic cavities, when short paths may play an important role in the scattering process. In particular, the validity of the model was investigated in relation with the statistical properties of the conductance in open chaotic cavities. In this article we investigate further the validity of the maximum-entropy model, by comparing the theoretical predictions with the results of computer simulations, in which the Schroedinger equation is solved numerically inside the cavity for one and two open channels in the leads; we analyze, in addition to the conductance, the zero-frequency limit of the shot-noise power spectrum. We also obtain theoretical results for the ensemble average of this last quantity, for the orthogonal and unitary cases of the circular ensemble and an arbitrary number of channels. Generally speaking, the agreement between theory and numerics is good. In some of the cavities that we study, short paths consist of whispering gallery modes, which were excluded in previous studies. These cavities turn out to be all the more interesting, as it is in relation with them that we found certain systematic discrepancies in the comparison with theory. We give evidence that it is the lack of stationarity inside the energy interval that is analyzed, and hence the lack of ergodicity that gives rise to the discrepancies. Indeed, the agreement between theory and numerical simulations is improved when the energy interval is reduced to a point and the statistics is then collected over an ensemble. It thus appears that the maximum-entropy model is valid beyond the domain where it was originally derived. An understanding of this situation is still lacking at the present moment.

Stochastic gravitational wave measurements with bar detectors: dependence of response on detector orientation

The response of a cross-correlation measurement to an isotropic stochastic gravitational-wave background depends on the observing geometry via the overlap reduction function. If one of the detectors being correlated is a resonant bar whose orientation can be changed, the response to stochastic gravitational waves can be modulated. I derive the general form of this modulation as a function of azimuth, both in the zero-frequency limit and at arbitrary frequencies. Comparisons are made between pairs of nearby detectors, such as LIGO Livingston–ALLEGRO, Virgo–AURIGA, Virgo–NAUTILUS and EXPLORER–AURIGA, with which stochastic cross-correlation measurements are currently being performed, planned or considered.