Plasma oscillations in two-dimensional electron systems with a superstructure under Stark quantization conditions

The effect of quantizing electric field on plasma oscillations of two-dimensional electron gas in a system with a periodic potential has been theoretically investigated. The coupled-plasmon spectrum ω(q) is calculated for high temperatures (Δ ? T, where Δ is the conduction miniband width and T is temperature in energy units). The calculations are based on the quantum theory of plasma oscillations in the random-phase approximation, with allowance for the umklapp processes.     

Flux quantization in a hollow superconducting cylinder with a solenoid inside a cavity

The behavior of a hollow superconducting cylinder with a long solenoid inside a cavity is considered within the framework of the Ginzburg-Landau theory. The general form is found of the thermodynamic potential of the system, which describes its behavior under the influence of the solenoid's field. It is shown that the magnetic field appears inside a cavity, when the solenoid's flux is not zero. The total flux in the system changes by jumps, due to the effect of flux quantization. The dependence of the superconducting order parameter on the solenoid's flux is found, the phase diagram of the superconducting states is analyzed. The hysteresis transitions in the system are investigated, as well as oscillations of the critical temperature and of the specific heat of the cylinder. The connection with the paper of G. Kunstatter, M. Revzen, and L. E. H. Trainor (Ann. Phys. (N.Y.)145 (1983), 329), where the corresponding problem was first touched upon, is discussed.     

What does Finite Volume-based implicit filtering really resolve in Large-Eddy Simulations?

The study illustrated in this paper completes the topics initially investigated in Ref. [42], the aim being here to analyze the role of the integral-based Finite Volume (FV) discretizations in Large Eddy Simulations that exploit the implicit filtering approach. Specifically, a theoretical study on the effective shape and length of three-dimensional filters induced by some FV-based flux reconstructions is the object of this paper. For any integral-based flux reconstruction, one gets always an approximation of the top-hat filter kernel. This is not the case of the filters induced by the differential-based Finite Difference operators, such as those reported and analyzed in Refs.  and . Considering the sub-filter resolution parameter Q = Δ_eff/h, being Δ_eff the effective filter width and h the computational grid size, allows us discerning the effective measure of the approximate built-in top-hat filter. The induced shape and width is analyzed by means of a modified wavenumber-like analysis that is developed in the 3D Fourier space. Several evaluation criteria applied on different schemes are considered and the differences in terms of either velocity or flux interpolations on staggered or non-staggered grids are analyzed. Conclusions are reported that, depending on the using of either the integral or the differential form of the filtered equations, the induced numerical filter is or is not a congruent approximation of the exact top-hat transfer function for some value Q. The need of a suitable estimation of the sub-filter parameter Q is assessed from several real LES computations, that make use of the new integral-based version of the eddy-viscosity dynamic modeling presented in Ref. [42]. In fact, it is shown that the test-filtering length has to be carefully chosen as a function of the FV-based induced filter.     

Giant quantum oscillations of acoustoelectric current in Bi

In single crystals of Bi with resistivity ratio R₂₉₃/R_4.2 ≈ 300 by a helium temperature at frequencies 500 MHz of longitudinal sonic wave detected and investigated the longitudinal acoustoelectric effect.In strong magnetic fields if the condition $\text{h}\text{?}$ Ω ? kT,ql ? 1 Ω — cyclotron frequency, k — Boltzman constant) for directions H 6 q 6 y (y— a bissector crystal axis) and H 6 q 6 z (z — a triagonal crystal axis) is fulfilled, giant quantum oscillations of longitudinal acoustoelectric current are detected. Sign of current oscillations is determined by the type of current carriers.     

Instability of electromagnetic waves in transversely magnetised semiconductor-plasmas

Using the hydrodynamic model of plasmas the general dispersion relation is derived in the collisiondominated regime when a d.c. magnetic field is applied (Y-axis) transversly to the propagation vector k (Z-axis), and the d.c. electric field is inclined to the Z-axis in the X-Z plane. The dispersion relation is solved for intrinsic and extrinsic semiconductors to explore the possibility of wave instability. The threshold conditions of wave oscillations are obtained. In n-InSb the frequency of the oscillation attains a maximum value when the electron cyclotron frequency is equal to the electron collision frequency. In intrinsic InSb instability is possible only in the long wavelength region for E₀ ? 10 kVm^?1 when B₀> 0.2 T, while for lower values of B₀, E₀ should be greater 20kVm^?1. The energy dependent collision frequency has a significant effect on the threshold frequency of oscillation.     

Conductivity of carbon nanotubes in a longitudinal magnetic field

Multiwall carbon nanotubes exhibit oscillations of magnetoresistance with the period Φ₀=hc/2e [A. Bachtold, C. Strunk, J.-P. Salvetat, et al., Nature 397, 673 (1999)]. This effect is analogous to the Sharvin effect for a normal metal [D. Yu. Sharvin and Yu. V. Sharvin, Pis’ma Zh. Éksp. Teor. Fiz. 34, 285 (1981)]. It is shown that, along with the magnetoresistance peaks corresponding to the flux values that are multiples of Φ ₀, additional peaks with a period three times shorter can be observed in carbon nanotubes.     

Fast stray field computation on tensor grids

A direct integration algorithm is described to compute the magnetostatic field and energy for given magnetization distributions on not necessarily uniform tensor grids. We use an analytically-based tensor approximation approach for function-related tensors, which reduces calculations to multilinear algebra operations. The algorithm scales with N^4/3 for N computational cells used and with N^2/3 (sublinear) when magnetization is given in canonical tensor format. In the final section we confirm our theoretical results concerning computing times and accuracy by means of numerical examples.     

Path-length dependent flux from random walk theory

Calculation of the flux Ψ(R, s) due to a point isotropic source in an infinite medium, as a function of the distance R and actual pathlength s is treated as a random walk problem. In the case of isotropic scattering, this method is shown to lead to a standard transport-theoretical result, for the integrated flux. However, for Ψ(R, s) far from the source, the random walk theory predicts a modified maxwellian form.     

Geometric conservation law and applications to high-order finite difference schemes with stationary grids

The geometric conservation law (GCL) includes the volume conservation law (VCL) and the surface conservation law (SCL). Though the VCL is widely discussed for time-depending grids, in the cases of stationary grids the SCL also works as a very important role for high-order accurate numerical simulations. The SCL is usually not satisfied on discretized grid meshes because of discretization errors, and the violation of the SCL can lead to numerical instabilities especially when high-order schemes are applied. In order to fulfill the SCL in high-order finite difference schemes, a conservative metric method (CMM) is presented. This method is achieved by computing grid metric derivatives through a conservative form with the same scheme applied for fluxes. The CMM is proven to be a sufficient condition for the SCL, and can ensure the SCL for interior schemes as well as boundary and near boundary schemes. Though the first-level difference operators δ₃ have no effects on the SCL, no extra errors can be introduced as δ₃ = δ₂. The generally used high-order finite difference schemes are categorized as central schemes (CS) and upwind schemes (UPW) based on the difference operator δ₁ which are used to solve the governing equations. The CMM can be applied to CS and is difficult to be satisfied by UPW. Thus, it is critical to select the difference operator δ₁ to reduce the SCL-related errors. Numerical tests based on WCNS-E-5 show that the SCL plays a very important role in ensuring free-stream conservation, suppressing numerical oscillations, and enhancing the robustness of the high-order scheme in complex grids.     

Effects of band structure and matrix element on RKKY interaction

The effects of band structure and matrix elements on the RKKY interaction J(R) are separately investigated. When the Fermi surface has planes perpendicular to R, effects appear on the period of oscillation, the phase shift and the amplitude of J(R). The applicable region of the asymptotic form for large R and the validity of the free electron approximation are also examined. If there are no tangential planes perpendicular to R, it is found that: 1) when two interacting localized spins are on lattice points in the crystal, exponential damping appears even for the constant matrix element model and the matrix element effects introduce competing terms causing a sign change; 2) when one of the spins is at an interstitial position, the constant matrix model gives a weaker J(R) ∝ R^-2 damping, but the character of this term changes into the exponential damping by taking into account matrix elements.     

The Vlasov equation for systems with velocity dependent interactions

This work contains a discussion of the Vlasov approximation for the system of particles interacting not only via the pair-wise central potential, but also via the velocity dependent interactions (V.D.I). The VDI are assumed to be similar in nature to those encountered in the classical plasma when the higher order in ($\text{ν}\text{c}$) corrections to the Coulomb forces are taken into account. Using the Klimontovich formulation of the many-body dynamics, we derive the general equation of motion for the exact one-particle distribution function N(r, v, t and we discuss the Vlasov approximation to this equation in some detail. The linearization of the Vlasov equation and the derivation of the dispersion relations for longitudinal and transverse waves are also presented while the detailed analysis of the solutions and of the stability problem is postponed to the following publication.     

Das Fluktuationsspektrum von Elektronen in einem stationären Nichtgleichgewichtszustand

The Boltzmann equation is used to calculate the time correlation function and the fluctuation spectrum for electrons obeying classical statistics. The stationary joint distribution for one electron to be initially ink ₀=k(0) and finally ink=k(t) is given by the product of the conditional probability and the stationary distribution. These quantities can be found from the Boltzmann equation if there exists, for any initial distribution, a unique solution which satisfies the Markov equation and tends to a stationary solution for large times under stationary conditions. It is proved that these conditions hold for linear collision operators and in the relaxation approximation. General operator expressions for the fluctuation spectrum and the differential conductivity in a stationary electric field are given, which can be evaluated within the usual approximation schemes known for the stationary, nonequilibrium solutions of the Boltzmann equation. In equilibrium they reproduce the classical fluctuation dissipation theorem. In a nonequilibrium state they define a noise temperature depending on the field. In the relaxation approximation and for polynomial band structure the exact solution can be found. For parabolic and biparabolic spherical bands the result is discussed explicitly.     

On the intensity of shock-initiated magnetoelastic oscillations arising in iron borate single crystals during pulsed magnetizing or magnetization-switching processes

The intensities of magnetoelastic oscillations accompanying pulsed 180° and 90° magnetization switching of iron borate single crystals as well as pulsed magnetization of the crystals from a demagnetized state (with zero total magnetic moment) are compared for the first time. The amplitude A ₁ of the oscillations of the signal obtained from the experimental sample by the induction method is adopted as a measure of the intensity of the magnetoelastic oscillations. It is found that for the same pulse heights of the magnetic field H exciting the magnetization-switching or magnetizing process, the amplitudes A ₁ of the oscillations observed in 90° magnetization-switching and initial-magnetization processes have practically the same value, which is $\sqrt 2 $ times smaller than the amplitude of the oscillations obtained in 180° magnetization switching (reversal). It is concluded on the basis of the result obtained that the intensity of the magnetoelastic oscillations is virtually independent of the initial state of the single crystal and is determined mainly by the energy density ΔM·H acquired by the magnetic subsystem of the crystal from the external field (ΔM is the change in magnetization). Hence it follows that when iron borate is used in fast modulators for Mössbauer γ rays it is preferable to use the 90° magnetization-switching regime rather than the magnetization regime as has been done until very recently.     

Dynamic phenomena connected with magnetic and antiferroelectric interactions in trirutiles

Dynamic effects caused by the magnetoelectric and antiferroelectric interactions in tetragonal antiferromagnets are studied. The analysis is based on the example of trirutiles that are a series of antiferromagnets with different exchange structures and orientation states. We are mainly dealing with the excitation by an alternating electric field E(t) of spin waves typical of these magnets (antiferroelectric resonance) and the nuclear magnetoelectric resonance connected with these interactions. In the first case, special emphasis is placed on specific magnons (antimagnons), where only the antiferromagnetism vectors L take part in oscillations, whereas the total ferromagnetism vector M remains unchanged. The nuclear magnetoelectric resonance can be generated by oscillations of both L and M caused by field E(t). In this way, the field contributes to the hyperfine field, which acts on the nuclear spins. It is shown that the magnetic and antiferroelectric interactions in the dynamics can manifest themselves both at high (usually, exchange) frequencies ωw_E (antiferroelectric resonance) and at rather low nuclear frequencies of ω_n?ω_E. Particular cases of magnetic structures (phases) are considered where field E(t) can excite not only antimagnons, but also quasiantiferromagnons that have lower eigenfrequencies than those of quasimagnons (relativistic and semirelativistic).     

Longitudinal relaxation spectra of the transverse Ising model close to Tc

The correlative effects of the nature of the interaction and of the method of calculation on the shape of the longitudinal relaxation function (LRF) for the transverse Ising model are analysed. The LRF is calculated in two ways: (i) its continued fraction representation within the three pole approximation (TPA); and (ii) the resolution of kinetic equations derived for the correlation functions beyond the random phase approximation (RPA). The effects of the nature of the interaction on the LRF spectral characteristics are investigated using an interaction made of three variable contributions: uniaxial dipolar, isotropic infinite range and anisotropic nearest-neighbour interactions. Contrary to the TPA, the kinetic-equation-method (KEM) leads to LRF's exhibiting a three peak structure for every q-value except q = 0 (q = 0_⊥ if the interaction is of dipolar nature) whatever the interaction. The approximations underlying both methods are specified and discussed. Comments on recent neutron scattering experiments on Li Tb_pY_1-pF₄ by Youngblood et al. are made.     

Hybrid mesons in the context of the relativistic equation

The flux tube model of hybrid mesons is studied in the context of the relativistic equation in the adiabatic approximation. The moment of inertia of the rigid-rod flux tube is considered in the kinetic part of the interaction. The nonrelativistic and relativistic one scalar bead flux tube is integrated numerically and compared with the adiabatic flux tube small oscillation approximation. The relativistic scalar bead picture suggests that the lowest gluonic excitation of a massive gluon is color octet q q? pair while the conventional mesons are color singlet as usual. We estimate the lowest hybrid charmonium states as 1₁ P = 4.17 ± 0.03 and 1₁D = 4.39±0.05 GeV with color octet qq pair and as 1₁P = 3.78± 0.05 and 1₁D = 4.04±0.09 GeV with color singlet q q? pair. These results are also confirmed by the adiabatic flux tube small oscillation approximation when the hybrid energy gap is adjusted phenomenologically to M _Hc = M _ground + 1GeV.     

On the calculation of multiphoton transition amplitude in intense electromagnetic radiation

It has been shown that if all order corrections are taken into account in the momentum translation approximation there would not be any contribution to the multiphoton transition amplitude due to momentum translation factor exp (ie A·x). Thus the calculations performed using the momentum translation approximation method, without any consideration to higher order corrections, are incorrect.     

“Soft” modes of the excitation spectrum constructed on perturbations of the Abrikosov lattice with a single flux quantum in the unit cell

We have analyzed the spectrum of gapless excitations emerging upon the perturbation of the Abrikosov lattice with a single flux quantum in the unit cell. Superconductors with Ginzburg–Landau parameter κ close to unity are of special interest. We have determined the spectrum of gapless excitations close to zeroth shear modes for an arbitrary angle ? between the unit cell vectors. Analysis of the excitation spectra of triangular and square lattices with a single flux quantum in the unit cell has shown that solutions with a number of flux quanta greater than one exist at least in the range of parameters κ close to unity (κ > 1) and give smaller values of the free energy as compared to its values for a triangular lattice with a single flux quantum. For small values of momentum k (in the k ² approximation), the excitation spectrum of the “transverse” mode in the triangular lattice is independent of the direction of the momentum lying in the plane perpendicular to the magnetic field. For the square lattice (? = π/2), the transverse mode is anisotropic in the k ² approximation also.     

Kinetic theory of reacting systems

In this paper transport processes of reacting systems are investigated, based on the Boltzmann equations. The Boltzmann equations are solved by means of Grad's moment method to thirteen moments and some formal results are obtained for transport properties. It is shown that the rate coefficients are quadratic functions of hydrodynamic fluxes and are in the form

where

are the scalar moments associated with the reaction and q, J, Π are heat flux, material flux and traceless symmetric stress tensor. k⁽⁰⁾_i is the usual local equilibrium formula for reaction rate constant. Iterative solutions for the equations of change for

, q, J and Π are obtained from which transport coefficients are calculated for the reacting system. It is shown that the solutions, when specialized to nonreacting mixtures, lead to results for the transport coefficients which are exactly in agreement with the Chapman-Enskog theory results. The modifications of the transport coefficients due to reactions are obtained from the iterative solutions and the bracket integrals necessary for their calculations are explicitly given in an appendix.     

Decoupling potentials for the three-body final state Schrödinger equation of knockout reactions

In the conventional distorted wave impulse approximation (DWIA) approach the three-body final state of a knockout reaction is decoupled by assuming a plane wave form for the coupling term. The influence of this decoupling approximation on the analyses of cluster knockout reactions has been investigated for a test case where the exact solution is obtainable. A proper treatment of the coupling term causes large oscillations in the effective distorting optical potentials for the decoupled Schrödinger equation. These decoupling potentials depend strongly not only on the partial wave angular momentum,l but also on their azimuthal projection,m.