Fractional Integro-Differential Equations for Electromagnetic Waves in Dielectric Media

We prove that the electromagnetic fields in dielectric media whose susceptibility follows a fractional power-law dependence in a wide frequency range can be described by differential equations with time derivatives of noninteger order. We obtain fractional integro-differential equations for electromagnetic waves in a dielectric. The electromagnetic fields in dielectrics demonstrate a fractional power-law relaxation. The fractional integro-differential equations for electromagnetic waves are common to a wide class of dielectric media regardless of the type of physical structure, the chemical composition, or the nature of the polarizing species (dipoles, electrons, or ions)

表紙、裏表紙、奥付

In this work liquid helium-4 is studied for the first time within the framework of the so-called static fluctuation approximation. This is based on the replacement of the square of the local-field operator with its mean value. A closed set of nonlinear integral equations is derived for weakly as well as for strongly interacting systems. This set is solved numerically by an iteration method for a realistic interhelium potential. The thermodynamic properties are then obtained for both the weakly interacting system, liquid 4He in Vycor glass, and the strongly interacting system, liquid 4He. It turns out, however, that the present quadratic-fluctuation approximation is valid in the latter, strongly interacting case only in the low-temperature limit (≤0.15 K). Our results are presented in a set of figures. The role of the interaction is emphasized and the functional dependence of key thermodynamic quantities on the temperature is derived for both weakly and strongly interacting 4He systems. © 2001 Plenum Publishing Corporation

Identification of the generalized Weibull distribution in wind speed data by the Eigen-coordinates method

The real distributions of local wind speed obtained from random temporal series have been analyzed in the framework of the new Eigen-coordinates method (ECs), which helps to identify a true hypothesis with high level of authenticity. The season variations of the wind speed have been registered in Fjage (Jordan) and considered as initial data. It has been shown that histograms of the local wind speed were precisely described by the generalized Weibull model and the distribution model suggested by C. Tsallis should be rejected for present case. The possibilities and recommendations for the application of the ECs method to identify the theoretical curves needed for description of experimental data containing significant deviations are discussed. It has been shown that the ECs method could be used in these cases as a general approach and could be applied for analysis of temporal random series of different nature. PACS: 02.60.Ed., 02.60.Pn., 06.20.Dk., 07.05.Kf., 07.05.Rm. © 2002 Elsevier Science Ltd. All rights reserved

Thermodynamics of the interacting Fermi-system in the Static Fluctuation Approximation

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the frame of the static fluctuation approximation (SFA) method. This method based only on the single and controllable approximation allows to obtain the so-called far-distance equations (FDEs). These equations connecting the quantum states of a Fermi particle with variables of the local field operator contains all necessary information related to calculation of the desired correlation functions and basic thermodynamic parameters of the many-body system considered. The basic expressions for the mean energy and heat capacity for electron gas at low temperatures in the limit of high density were obtained. All expressions are given in the units of r_s,where r_s determines the ratio of a mean distance between electrons to the Bohr radius a_0. In these expressions we calculated the terms of the order r_s and r_s^2, correspondingly. It was shown also that the SFA allows to find the terms related with high orders of the decomposition with respect to the parameter r_s.Comment: 22 pages, 5 figure

Implementation of Fault-tolerant Quantum Logic Gates via Optimal Control

The implementation of fault-tolerant quantum gates on encoded logic qubits is considered. It is shown that transversal implementation of logic gates based on simple geometric control ideas is problematic for realistic physical systems suffering from imperfections such as qubit inhomogeneity or uncontrollable interactions between qubits. However, this problem can be overcome by formulating the task as an optimal control problem and designing efficient algorithms to solve it. In particular, we can find solutions that implement all of the elementary logic gates in a fixed amount of time with limited control resources for the five-qubit stabilizer code. Most importantly, logic gates that are extremely difficult to implement using conventional techniques even for ideal systems, such as the T-gate for the five-qubit stabilizer code, do not appear to pose a problem for optimal control.Comment: 18 pages, ioptex, many figure

Influence of self-similar collisions on the Doppler broadening

A self-similar collision model for the motion of radiating particles in a perturbed gas is suggested. The influence of effects of self-similar collisions on the shape of a spectral line in the Doppler regime is considered in the framework of classical Fourier integral theory. In the limiting case when the self-similar character of collisions is not taken into account the self-similar collision model becomes identical to the Galatry diffusion model. The general formula for the distribution function of the radiating particles in the self-similar model and a new correlation function in the impact approximation are derived. It is shown that the self-similar collision mechanism in the Doppler regime leads to additional spectral line narrowing

An algorithm for determining dispersion and Doppler line widths from limited experimental data

We present an algorithm that allows the efficient determination of the dispersion and Doppler contributions to a Voigt profile from limited experimental data. For this purpose, we use the measured intensity profiles, as well as their first and second derivatives. © 1991

Identification of a new function model for the AC-impedance of thermally evaporated undoped selenium films using the Eigen-coordinates method

The experimental AC-impedance data of undoped amorphous and polycrystalline selenium films were taken at T = 300K in the frequency range 100 Hz-10 kHz in the dark and under band-gap illumination. The data were analyzed using the Eigen-coordinates method in conjunction with a 'separation' procedure without prior use of equivalent circuits. A unified circuit model with generalized impedances was recognized to parameterize well the observed AC-impedance behavior. The features of this electrical model were linked to the fractality of the heterogeneous structural regions in these selenium specimens via one or two recap elements, each represented by a complex impedance of fractional power-law frequency behavior. These recap elements reflect the electric properties of scale-invariant circuits of self-affine normal (ideal) resistor-capacitor (RC) cells of the Cauer/Forster type. © 2001 Elsevier Science B.V. All rights reserved