Quantum electrodynamics in a laser and the electron laser collision

Quantum electrodynamics in a laser is formulated, in which the electron–laser interaction is exactly considered, while the interaction of an electron and a single photon is considered by perturbation. The formulation is applied to the electron– laser collisions. The effect of coherence between photons in the laser is therefore fully considered in these collisions. The possibility of γ-ray laser generation by use of this kind of collision is discussed.     

Influence of nonlinear interactions on the development of instability in hydrodynamic wave systems

The problem of the development of shear instability in a three-layer medium simulating the flow of a stratified incompressible fluid is considered. The hydrodynamic equations are solved by expanding the Hamiltonian in a small parameter. The equations for three interacting waves, one of which is unstable, have been derived and solved numerically. The three-wave interaction is shown to stabilize the instability. Various regimes of the system’s dynamics, including the stochastic ones dependent on one of the invariants in the problem, can arise in this case. It is pointed out that the instability development scenario considered differs from the previously considered scenario of a different type, where the three-wave interaction does not stabilize the instability. The interaction of wave packets is considered briefly.     

线性聚焦和线性散焦效应对空间光孤子间相互作用的影响

考虑非均匀一维自聚焦介质的横向不均匀性,利用非线性薛定谔方程满足的守恒律给出了相邻空间孤子间隔的解析式,并对空间孤子之间的相互作用进行了数值模拟.结果表明,线形聚焦效应增强了空间孤子之间的相互作用;而线形散焦效应减弱了空间孤子之间的相互作用.当不考虑介质横向不均匀时,空间孤子之间发生周期性的碰撞.线性散焦效应使相邻空间孤子之间的间隔随传输距离发生周期性的变化,但孤子之间并不发生碰撞.线性聚焦效应使相邻空间孤子随传输距离发生周期性的碰撞,线性聚焦效应具有压制损耗使相邻空间孤子间隔变大的作用.     

Field ionization processes in field ion microscopy

The processes of field ionization are considered by the time dependent perturbation theory. The metal wave function to be occupied by a tunneling electron from a monovalent atom is approximated by the tight-binding method. The system considered is hydrogen imaging a tungsten-type metal. The (001) crystallographic plane with an interatomic spacing of 3.16 Å and an externally applied electric field of 2.3 V/Å is considered for numerical results. Image formation mechanisms of field ion microscopy are qualitatively discussed.     

Analysis of Frequency Selective Surfaces with Metallic and Dielectric Losses at Millimeter Wave Range

In this paper, a theoretical analysis of scattering from a doubly frequency selective surfaces (FSS) with dielectric and metallic losses in the millimeter wave range is presented. The theoretical analysis involves the solution of the electric field integral equation relating the induced current in the FSS in the presence of anisotropic dielectric layers. The method of moment is employed to obtain numerical results. The frequency selective surface structure considered is composed by conducting patch elements sandwiched between two anisotropic dielectric layers. Three different anisotropic materials are considered: Epsilam-10, Alumina, and Sapphire. The sapphire presents low losses when compared with the other two dielectric materials. The most common metals, as copper and aluminum, are considered in this analysis. None significant metallic losses were observed for any considered metal. Numerical results are presented for the scattering characteristics and for dielectric and metallic losses parameters.     

On the relation between the fractional Brownian motion and the fractional derivatives

The definition and simulation of fractional Brownian motion are considered from the point of view of a set of coherent fractional derivative definitions. To do it, two sets of fractional derivatives are considered: (a) the forward and backward and (b) the central derivatives, together with two representations: generalised difference and integral. It is shown that for these derivatives the corresponding autocorrelation functions have the same representations. The obtained results are used to define a fractional noise and, from it, the fractional Brownian motion. This is studied. The simulation problem is also considered.     

Light transmission in a finely divided scintillator

The propagation of scintillation light is considered for a granular detector bounded by surfaces differing in reflectivity. The optimal parameters of the detector are considered; a comparison is made with experiment.     

Multi-switching dual compound synchronization of chaotic systems

A novel multi-switching dual compound synchronization scheme is proposed for chaotic systems which has not been investigated so far. The goal is to design appropriate controllers by using Lyapunov stability theory and nonlinear control to establish the asymptotically stable synchronized state for six drive and two response systems. Multi-switching dual compound synchronization can be considered as an extension of multi-switching dual combination synchronization. An example is presented to elaborate the proposed scheme where Lorenz, Chen, Lu systems are considered as master systems and T system is considered as slave system. The results obtained by theoretical and graphical analysis are in excellent agreement.     

Evaluation of liquid-vapour density profiles of associating fluids: A density-functional approach

The structure of liquid-gas interface of associating Lennard-Jones particles is studied using the density-functional theory and the Monte Carlo simulation. The model with one bonding site per particle is considered. It is shown that the considered version of the density functional is quite successful in predicting the gas-liquid density profile.     

Synchronous behavior of coupled systems with discrete time

The dynamics of one-way coupled systems with discrete time is considered. The behavior of the coupled logistic maps is compared to the dynamics of maps obtained using the Poincaré sectioning procedure applied to the coupled continuous-time systems in the phase synchronization regime. The behavior (previously considered as asynchronous) of the coupled maps that appears when the complete synchronization regime is broken as the coupling parameter decreases, corresponds to the phase synchronization of flow systems, and should be considered as a synchronous regime. A quantitative measure of the degree of synchronism for the interacting systems with discrete time is proposed.     

Mixing and Lyapunov exponents of chaotic systems

Mixing of phase trajectories in chaotic systems is considered. The mixing rate is analytically estimated, and an algorithm for its computation in numerical experiment is descried. A relation between the local mixing rate and local Lyapunov exponents is considered. The applicability of the algorithm is demonstrated with a number of chaotic systems.     

Novel approach for modified forms of Camassa-Holm and Degasperis-Procesi equations using fractional operator

In the present study, we consider the q-homotopy analysis transform method to find the solution for modified Camassa-Holm and Degasperis-Procesi equations using the Caputo fractional operator. Both the considered equations are nonlinear and exemplify shallow water behaviour. We present the solution procedure for the fractional operator and the projected solution procedure gives a rapidly convergent series solution. The solution behaviour is demonstrated as compared with the exact solution and the response is plotted in 2D plots for a diverse fractional-order achieved by the Caputo derivative to show the importance of incorporating the generalised concept. The accuracy of the considered method is illustrated with available results in the numerical simulation. The convergence providence of the achieved solution is established in $\hslash $-curves for a distinct arbitrary order. Moreover, some simulations and the important nature of the considered model, with the help of obtained results, shows the efficiency of the considered fractional operator and algorithm, while examining the nonlinear equations describing real-world problems.     

Pair creation by a non-local potential

The probability of pair creation by a separable and non-local potential is considered following the Schwinger approach. It has been found that this probability is null. As a particular case, the separable δ-potential is considered and the probability is also found null.     

一维三原子分子的振动

考虑三原子分子的振动问题,利用线性代数的化标准型理论,获得该振动系统简正频率的数学表达式,并讨论了几种特殊的情况.     

On the absence of purely electronic phase transition in extended Falicov-Kimball model

The Falicov-Kimball model extended by the hybridization between the localized and band electrons is considered in the approximation valid for the narrow band. The limit of infinite Coulomb repulsion G is considered. In spite of the fact that the approximation involved favour the abrupt change of the occupation number of ?-states we have not found any discontinuous solution. This suggests that the first order phase transition in SmS can not be considered as being or purely electronic nature.     

Baryogenesis at the electroweak scale

The generation of the baryon asymmetry of the universe is considered in the standard model of the electroweak theory with simple extensions of the Higgs sector. The propagation of quarks of masses up to about 5 GeV are considered, taking into account their markedly different dispersion relations due to propagation through the hot electroweak plasma. It is shown that the contribution of the b quark to the baryon asymmetry can be comparable to that for the t quark considered earlier.     

Particle clustering and Mott transitions in nuclear matter at finite temperature: (I). Method and general aspects

The thermodynamic state of nuclear matter as regards dependence on density and temperature is considered. Expressions for the association degree are derived describing the ratio of nuclear matter which is clustered to bound states. The problem of two nucleons imbedded in the surrounding nuclear matter is considered with the help of the Bethe-Goldstone equation for thermodynamic Green functions. The two-particle energy shift due to the effective nuclear matter hamiltonian is considered in a Hartree-Fock approximation, and a Mott density is obtained so that for densities of nuclear matter higher than the Mott density bound states cannot exist. With a simplified effective two-nucleon interaction the association degree is calculated as a function of the nucleon density and the temperature.     

Effect of pinhole roughness on light diffraction

Light diffraction on an arbitrarily shaped pinhole in an infinite-conductivity screen plane is considered within Kirchhoff-Helmholtz scalar theory. The average pinhole diameter is comparable to the incident light wavelength λ = 633 nm. The case of normal incidence is considered. The amplitude and phase characteristics of the diffracted field are calculated on the spherical surface.     

Investigating RF and microwave nonlinear magnetoelastic interactions in a three-layer structure

The problem of hypersound excitation in a structure consisting of three magnetic layers is considered. Motion equations and boundary conditions for the components of magnetization and elastic displacement when there is an arbitrary angle of magnetization vector precession are obtained. The development of oscillations over time in an alternating field is considered.