Quadratic Shift Research Articles

The post-Newtonian mean anomaly advance as further post-Keplerian parameter in pulsar binary systems

The post-Newtonian gravitoelectric secular rate of the mean anomaly ℳ is worked out for a two-body system in the framework of the General Theory of Relativity. The possibility of using such an effect, which is different from the well known decrease of the orbital period due to gravitational wave emission, as a further post-Keplerian parameter in binary systems including at least one pulsar is examined. The resulting effect is almost three times larger than the periastron advance $\dot{\omega}$ . E.g., for the recently discovered double pulsar system PSR J0737-3039 A+B it would amount to −47.79 deg yr−1. This implies that it could be extracted from the linear part of a quadratic fit of the orbital phase because the uncertainties both in the linear drift due to the mean motion and in the quadratic shift due to the gravitational wave are smaller. The availability of such additional post-Keplerian parameter would be helpful in further constraining the General Theory of Relativity, especially for such systems in which some of the other post-Keplerian parameters can be measured with limited accuracy. Moreover, also certain pulsar-white dwarf binary systems, characterized by circular orbits like PSR B1855+09 and a limited number of measured post-Keplerian parameters, could be used for constraining competing theories of gravity.

Comparison of electric field effects on carriers between spherical quantum dots and cylindrical quantum wires

We investigate the effect of an electric field applied to two systems; a spherical quantum dot and a cylindrical quantum wire. In the latter system the field is applied perpendicular to the cylinder axis. We are interested on the energy ground state of carriers in the quantum dot and wire using an infinite confining potential well model. We perform a variational calculation for both systems and for low electric fields we find a quadratic shift of the energy levels with the electric field. For strong fields the Stark shift of the energy groundstate increases almost linearly with the electric field. In order to compare the results of both systems, we choose the radii of the sphere and the cylinder to be equal. For same radii the Stark shift of the sphere is smaller than that of the cylinder. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Effect of electric field on the probability of optical transitions in InGaAs/GaAs quantum wells observed by photo‐ and electroreflectance methods

AbstractThe influence of an electric field on the energy spectrum and the probability of optical transitions in InGaAs/GaAs single quantum wells (QWs) of different widths has been investigated with photo‐ and electroreflectance techniques. The electric field in the area of a QW is varied in a wide range and controlled by well‐defined Franz–Keldysh oscillations. A quadratic red shift of electroreflectance features concerned with interband excitonic transitions in QWs is observed. The electric field dependence of the intensity of these features and calculated data for the probability of optical transitions are compared. There are some field values when transitions that are symmetry‐forbidden in zero field are much stronger than symmetry‐allowed transitions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Zeeman effect of single-molecule lines

The spectral line shifts induced by a magnetic field were measured for single terrylene molecules in the Shpol’skiĭ matrix n-hexadecane at liquid-helium temperatures. Quadratic red shifts with magnitudes between about 0 and −8 MHz/T 2 were observed. The red shift is tentatively ascribed to a predominant contribution of van Vleck paramagnetism. The broad variation between the molecules is due to the random molecular orientations in different samples. The magnitude of the shift is much smaller than in porphyrins, since terrylene does not have two closely spaced excited states.

Effects of high pressure on the photoluminescence transitions of excitons in α‐PTCDA (perylene tetracarboxylic dianhydride) crystals

AbstractWe report investigations of the photoluminescence (PL) spectrum of α‐PTCDA single crystals at 11 K and 300 K as a function of applied pressures to 54 kbar carried out using a diamond‐anvil cell with annealed methanol‐ethanol medium. The effects of pressure are observed on several excitonic PL features principally associated with: an excimer transition for the 300 K spectra, or an indirect Frenkel exciton and charge transfer exciton transitions (between stacked molecules in different unit cells) for the 11 K spectra. Under applied pressure, all of these features redshift at rates that are in general accord with the π – π* broadening caused by increasing overlap between PTCDA molecules, but with variations in pressure dependence, especially in the quadratic shifts, that derive from the specific character and Stokes‐shift mechanisms of the exciton transitions. The observed pressure behavior conforms to a recent model of the exciton transitions in α‐PTCDA based on a theoretical analysis of 1 atm time‐resolved PL experiments. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Spherical quantum dot under an electric field

We investigate the effect of an electric field applied to a spherical quantum dot on the energy groundstate of carriers in the quantum dot using an infinite confining potential well model. We perform a simple variational calculation for low electric fields and we find a quadratic shift of the energy levels with the electric field while for strong fields, the Stark shift of the energy groundstate increases almost linearly with the electric field. There is a transition for quasi-one dimensional to three-dimensional behavior when the dot radius is large. The comparison of our results with previous exact calculations is very good. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Sloped and bow‐tie speckles from a warped energetic landscape

A spatially inhomogeneous shift of the center-of-mass potential energy for excitons in a disordered nanostructure affects the directionally and temporally resolved speckle pattern in the secondary emission. It leads to a modification of both shape and orientation of the average speckle. We analyze the cases of linear and quadratic energy shift and find analytical expressions for the corresponding speckle correlation functions. The tilting of the correlation is given by the local energy gradient, while the correlation width dynamics is determined by the energy curvature. The speckle temporal shape is related to the local Rayleigh spectrum, whose broadening due to the potential energy modification is here investigated. These findings are confirmed by the agreement with full numerical simulations. Speckles provide therefore precise information also about systematic potentials affecting the exciton motion. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Transverse Stark effect of electrons in a semiconducting quantum wire

AbstractWe investigate the effect of an electric field applied tranversely to the axis of cylindrical symmetry of a cylindrical quantum wire on the ground‐state energy of the electrons in the wire using an infinite confining potential well model. For low electric fields, we find a quadratic shift of the energy levels with the electric field; while for strong fields, the Stark shift of the ground‐state energy increases almost linearly with the electric field. This increase is greater for wide wires, but for narrow wires, the Stark shift of the ground‐state energy does not change much with the electric field. Also, at higher electric fields, the Stark shift of the ground‐state energy increases with increasing wire radius. This will lead to the decrease of the effective bandgap of a semiconducting quantum wire with electric field. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The Three‐dimensional Kinematics of Water Masers around the Semiregular Variable RT Virginis

We report observations of water masers around the semiregular variable RT Virginis, which have been made with the Very Long Baseline Array of the National Radio Astronomy Observatory at five epochs, each separated by 3 weeks of time. We detected about 60 maser features at each epoch. Overall, 61 features, detected at least twice, were tracked by their radial velocities and proper motions. The three-dimensional maser kinematics exhibited a circumstellar envelope that is expanding roughly spherically with a velocity of 8 km s-1. Asymmetries in both the spatial and velocity distributions of the maser features were found in the envelope, but they were less significant than those found in other semiregular variables. Systematic radial velocity drifts of individual maser features were found with amplitudes of ≤2 km s-1 yr-1. For one maser feature, we found a quadratic position shift with time along a straight line on the sky. This apparent motion indicates an acceleration with an amplitude of 33 km s-1 yr-1, implying the passage of a shock wave driven by the stellar pulsation of RT Vir. The acceleration motion is likely seen only on the sky plane because of a large velocity gradient formed in the accelerating maser region. We estimated the distance to RT Vir to be about 220 pc on the basis of both the statistical parallax and model-fitting methods for the maser kinematics.

Higher-order Stark effect on single-molecules

Stark effect experiments have been performed on terrylene (Tr) and 2.3.7.8-di-(peri-naphthylen)-pyren (DPNP) molecules, both, in a n-hexadecane Shpol'skii matrix by single molecule spectroscopy technique at low temperatures. Electric field was applied to the samples in a range of up to 20 kV/cm. The differences between the dipole moments in the ground and first excited states have been calculated from the experimental data. The molecules showed mostly a linear shift in an external electric field and the contribution of the quadratic shift was rather small. A few molecules have demonstrated higher than linear or quadratic Stark effect, their spectra are presented and discussed.

Using non–time–series to determine supply elasticity: how far do prices change the Hubbert curve?

An important concern of OPEC’s work is to be able to understand how much supply of oil exists in different countries, in order to help better conserve oil. This paper extends M. King Hubbert’s oil production and discovery forecasting model (Hubbert, 1962), using a non–time–series cumulative discovery and production quadratic Hubbert curve and structural shift variables to model technology and regulation changes. The model can be used to determine better world oil supplies. Price is tested, to see how powerful it is for increasing or decreasing oil supply. Using a trend of cumulative production, instead of time, will help to better fix the supply elasticity with respect to price, which is shown to be very inelastic. An interesting question is whether cumulative discovery or production constitutes an I(2) variable. This paper explains that they are not I(2) variables.

Investigations of local currents in a semiconductor by single-molecule spectroscopy

Single organic molecules spread on a thin semiconductor film probe local electrical currents. For low DC voltages, we measure strong quadratic line shifts with thresholds at higher voltages. Under AC voltages, the shifts of most molecules display resonances between 10kHz and 1 MHz, with frequencies and shapes differing from molecule to molecule within the laser spot. For high enough DC voltages, auto-oscillations of the optical frequency can appear. These surprising effects do not arise from a standard Stark effect, nor from lattice heating, and might be related to current instabilities or slow recharging waves.

Weakly Nonlinear Oscillations Superimposed on Finite Circumferential Shear of a Compressible, Nonlinear, Viscoelastic, Isotropic Material

A study is presented of the weakly nonlinear oscillatory response of a compressible, nonlinear, viscoelastic, isotropic material. In its reference configuration, the material takes the form of a hollow concentric circular cylinder bonded to a fixed support at its inner boundary and to a rigid shell at its outer boundary. The cylinder is brought to a deformed equilibrium state in which the outer shell has been rotated through a finite angle about the axis of the cylinder. The material model used combines linear damping with a generalized Blatz-Ko model. The parameters in this model are chosen so that this static deformation consists of circumferential shear, without radial displacement, in which case the normal stresses are self-equilibrating and no local volume change is induced. The outer shell is then subjected to a sinusoidal rotational disturbance, and the subsequent motion of the cylinder is studied. It is found that due to dynamic effects the normal stresses are no longer self-equilibrated and radial motion is induced. The method of multiple scales is used to analyze the case where the motion is small but finite. This problem has unusual features for which special techniques for using the method of multiple scales were developed. The particular numerical results presented in this paper are for steady-state solutions to the problem of primary resonance of the first mode; however, the method is readily extendible. Results are given for both the purely elastic case and the case with linear damping. Many of the phenomena often associated with nonlinear oscillations occur, including mode saturation, the possibility of jump phenomena, and quadratic shift; however, the interpretation of these phenomena is complicated by the interaction of the spatial and temporal distributions of the deformation. These phenomena are examined by considering the influence of various system parameters on the moment that must be placed on the outer cylinder to maintain the motion. Of particular interest is the result that even a slight amount of compressibility has a significant impact on the motion.

Response of the Electric Field Gradient in Ion implanted BaTiO3 to an External Electric Field

AbstractSingle crystalline, ferroelectric BaTiO3 as material with the highest piezoelectric constants among the perovskites with ordered sublattices was implanted with 111In(111Cd). The electric field gradient at the Ti position was measured with perturbed γγ-angular correlation spectroscopy (PAC) while the crystal was exposed to an external electric field. A quadratic dependence could be observed: νQ(E) = (34.8(1) + 0.16(4) E/kV/mm + 0.080(2) E2/kV2/mm2) MHz. Point charge model calculations reproduce the linear change of Vzz, but not the quadratic term. The polarizability of the host ions of BaTiO3 is known to be nonlinear with respect to an electric field. The resulting quadratic shift of the electron density is reflected in the strength of the EFG.

Post‐Newtonian Theory for Precision Doppler Measurements of Binary Star Orbits

The determination of velocities of stars from precise Doppler measurements is described here using a relativistic theory of astronomical reference frames to determine the Keplerian and post-Keplerian parameters of binary systems. Seven reference frames are introduced: (1) the proper frame of a particle emitting light, (2) the star-centered reference frame, (3) the barycentric frame of the binary, (4) the barycentric frame of the Galaxy, (5) the barycentric frame of the solar system, (6) the geocentric frame, and (7) the topocentric frame of observer at the Earth. We apply successive Lorentz transformations and the relativistic equation of light propagation to establish the exact treatment of Doppler effect in binary systems both in special and general relativity theories. As a result, the Doppler shift is a sum of (1) linear in c-1 terms, which include the ordinary Doppler effect and its variation due to the secular radial acceleration of the binary with respect to observer; (2) terms proportional to c-2, which include the contributions from the quadratic Doppler effect caused by the relative motion of binary star with respect to the solar system, the motion of the particle emitting light and diurnal rotational motion of observer, orbital motion of the star around the binary's barycenter, and the orbital motion of the Earth; and (3) terms proportional to c-2, which include the contributions from redshifts due to fields of the star, the star's companion, the Galaxy, the solar system, and the Earth. After parameterization of the binary's orbit, we find that the presence of periodically changing terms in the Doppler shift enables us to disentangle different terms and measure, along with the well-known Keplerian parameters of the binary, four additional post-Keplerian parameters, which characterize (1) the relativistic advance of the periastron; (2) a combination of the quadratic Doppler and shifts associated with the orbital motion of the primary relative to the binary's barycenter and the companion's field, respectively; (3) the amplitude of the gravitational lensing contribution to the Doppler shift; and (4) the usual inclination angle of the binary's orbit, i. We briefly discuss the feasibility of practical implementation of these theoretical results, which crucially depends on further progress in the technique of precision Doppler measurements.

Transverse magnetic field studies in ZnSe/BeTe resonant tunneling structures

We report on resonant electron tunneling in ZnSe/BeTe double-barrier, single-quantum-well heterostructures under high magnetic fields. Current–voltage characteristics have been investigated in the presence of a magnetic field B perpendicular to the tunneling current (B⊥I). The effect of the field on the main resonance position as well as two additional features due to optical phonon assisted tunneling into the quantum well has been studied and analyzed. The peak bias voltage exhibits a quadratic shift with increasing magnetic field due to a Lorentz force acting on the tunneling electrons. The phonon peaks do not shift, because the transverse momentum is no longer conserved during this process.

Separation of quadratic and linear external field effects in high J quantum beats

We discuss quantum beats in electronically excited molecular states with high rotational angular momenta J appearing in time resolved fluorescence in conditions of quadratic and linear energy shift dependence on magnetic quantum number M and external field strength. Density matrix formalism is used to obtain in explicit form the expressions for time dependent fluorescence intensity after δ-function pulsed excitation. In case of pure quadratic Stark effect, which is typical for 1Σ state diatomics, excited state quantum beats for J≫1 exhibit a regular, or ‘‘grill’’ structure, consisting of narrow equidistant ‘‘principal’’ peaks with equal relative amplitudes on the exponential decay background. At linear polarized excitation the time intervals between the adjacent peaks are 2π/ω20, ω20 being the splitting frequency between coherently excited M-sublevels with M=2 and M′=0. If an admixture of linear contribution is present in field induced level shifts, the grill structure is superimposed by a single frequency harmonic modulation. A special geometry was found in which the quadratic beats are fully absent and the modulated grill pattern is brought into existence only by the influence of linear term. Such a case takes place when the light polarization vector in fluorescence is directed at 45° angle with respect to the exciting light polarization vector and yields the most sensitive way to separate quadratic and linear contribution. We considered the examples when the first order term appears by a combined action of electric and magnetic field, as well as due to the e–f level electric field induced mixing, with the parameters typical for the NaK molecule.

Two-photon spectroscopy of 1S-excitons in an AC electric field

1S-excitons in CuCl are studied by two-photon techniques in an AC electric field. The resonances show linear and quadratic energy shifts which can be explained by the Stark effect of valence bands and by the envelope Stark effect. The dipole matrix element of the Λ8-valence band and the Bohr radius of excitons in CuCl are determined.

High magnetic field studies of resonant tunneling via shallow impurities in δ-doped quantum wells

We have observed a new sub-threshold peak in the I(V) characteristics of double-barrier resonant tunneling structures. By investigating a range of intentionally δ-doped and control layers we can relate this peak to resonant tunneling through the bound state of a shallow donor impurity in the quantum well. We have studied the dependence of the voltage position of this peak on the magnitude of a magnetic field applied either parallel or perpendicular to the plane of the quantum well. In the parallel orientation the donor peak shifts slightly to lower voltage whereas the threshold of the continuum resonance shows the usual large quadratic shift to higher voltage. The amplitude of the donor-related peak is reduced in the presence of a magnetic field. We present a theoretical model to explain this behaviour and show how the results can be used to probe the spatial form of the impurity wavefunction in the quantum well.

Magnetic field induced indirect gap in a modulation doped quantum well

We report the first experimental evidence for the indirect fundamental band-gap developed when an in-plane magnetic field is applied to a wide, modulation-doped quantum well. In such structures, band bending may cause the lowest energy electron and hole states to be spatially separated, which leads to an induced indirect gap proportional to the field. The corresponding photoluminescence peak undergoes a large, roughly quadratic shift with field, a consequence of the behaviour of the allowed transitions involving thermalised holes and electrons with finite k. This characteristic strong diamagnetic shift is observed in spectra from both asymmetric AlGaAs/InGaAs/GaAs strained layer structures and a very wide symmetric InGaAs/InP lattice matched well. The experimental results are shown to be in good agreement with realistic self consistent calculations of the band-structure.