Relativistic motion of a free particle in a uniform gravitational field

The problem of the motion of a free particle in a uniform gravitational field is considered. A relativistic solution based on the assumption that the motion is a consequence of the curvature of spacetime is obtained. The results are compared with various results based on the assumption that spacetime is flat in a region in which the gravitational field is uniform. In the curved spacetime approach, if a particle is projected from a point in a uniform gravitational field, the vertical distance covered by the particle in infinite coordinate time is infinite, but the horizontal distance covered and the elapsed proper time of the particle are finite. If spacetime is assumed to be flat and the gravitational motion of a particle a consequence of a relativistic force proportional to the relative mass of the particle, then the results obtained for the motion of a particle in a uniform gravitational field are close to the curved spacetime results. All other assumptions, including the assumption that the motion of a particle in a uniform gravitational field is equivalent to the motion of a particle in a uniformly accelerating frame of reference, lead to results in serious disagreement with the curved spacetime results.     

Formation of a spiraling line defect and its meandering transition in a period-2 medium

The instability of a period-1 spiral wave resulting in a period-2 spiral wave with a line defect is investigated for the first time in a laboratory system. At the very onset the transition proceeds by an emergence of a spiraling line defect, "breathing" intermittently while retaining its symmetry of a period-1 spiral wave. With a further change in a control parameter, the line defect undergoes a meandering transition producing a compound tip trajectory, following a dynamic shape transition. The observed transitions have a strong analogy to the phase synchronization transition of two coupled nonlinear oscillators and the meandering transition of a period-1 spiral wave.     

Crossing bifurcations and unstable dimension variability

A crisis is a global bifurcation in which a chaotic attractor has a discontinuous change in size or suddenly disappears as a scalar parameter of the system is varied. In this Letter, we describe a global bifurcation in three dimensions which can result in a crisis. This bifurcation does not involve a tangency and cannot occur in maps of dimension smaller than 3. We present evidence of unstable dimension variability as a result of the crisis. We then derive a new scaling law describing the density of the new portion of the attractor formed in the crisis. We illustrate this new type of bifurcation with a specific example of a three-dimensional chaotic attractor undergoing a crisis.     

Synthesis of magnetic systems producing field with maximal scalar characteristics

A method of synthesis of the magnetic systems (MSs) consisting of uniformly magnetized blocks is proposed. This method allows to synthesize MSs providing maximum value of any magnetic field scalar characteristic. In particular, it is possible to synthesize the MSs providing the maximum of a field projection on a given vector, a gradient of a field modulus and a gradient of a field energy on a given directing vector, a field magnitude, a magnetic flux through a given surface, a scalar product of a field or a force by a directing function given in some area of space, etc. The synthesized MSs provide maximal efficiency of permanent magnets utilization. The usage of the proposed method of MSs synthesis allows to change a procedure of projecting in principal, namely, to execute it according to the following scheme: (a) to choose the sizes, a form and a number of blocks of a system proceeding from technological (economical) reasons; (b) using the proposed synthesis method, to find an orientation of site magnetization providing maximum possible effect of magnet utilization in a system obtained in (a). Such approach considerably reduces a time of MSs projecting and guarantees maximal possible efficiency of magnets utilization. Besides it provides absolute assurance in “ideality” of a MS design and allows to obtain an exact estimate of the limit parameters of a field in a working area of a projected MS.The method is applicable to a system containing the components from soft magnetic material with linear magnetic properties.     

Diachronic quantum action principle

Classical path and action are diachronic concepts in that they refer to many times instead of just one. The concept of a path is quantized into the concept of a propagation process between the initial preparation of and a measurement on a quantum system. A new quantum action is defined as a linear operator on the space of propagation processes, analogously to representing observables as linear operators on the ket and bra spaces. This quantization of paths and action results in a diachronic action principle: a variation of a dynamical propagation process is generated by the associated variation of the quantum action. The form of this principle is a candidate for the form of a dynamical principle of a theory without a classical time parameter.     

Electromagnetically induced transparency and light slowdown for Λ-like systems with a structured continuum

Electric susceptibility of a laser-dressed atomic medium is calculated for a model Λ-like system including two lower states and a continuum structured by a presence of an autoionizing state or a continuum with a laser-induced structure. Depending on the strength of a control field, it is possible to obtain a significant reduction of the light velocity in a narrow frequency window in the conditions of a small absorption. It is shown that increasing the values of the asymmetry parameters leads to an increase of the values of both real and imaginary parts of the medium susceptibility and to an increase of the width of the transparency window, compared with the case of a flat continuum. A smooth transition is shown between the case of a flat continuum and that of a discrete state serving as the upper state of a Λ system.     

Direct measurement of group dispersion of optical components using white-light spectral interferometry

We present a simple white-light spectral interferometric technique employing a low-resolution spectrometer for a direct measurement of the group dispersion of optical components over a wide wavelength range. The technique utilizes an unbalanced Mach-Zehnder interferometer with a component under test inserted in one arm and the other arm with adjustable path length. We record a series of spectral interferograms to measure the equalization wavelength as a function of the path length difference. We measure the absolute group refractive index as a function of wavelength for a quartz crystal of known thickness and the relative one for optical fiber. In the latter case we use a microscope objective in front and a lens behind the fiber and subtract their group dispersion, which is measured by a technique of tandem interferometry including also a Michelson interferometer.     

A Holographic Prism Based on Photo-Thermo-Refractive Glass: Requirements and Possibilities

A technology for multivalued holographic measurement of a plane angle—a holographic prism, which serves as the basis for a device for calibrating the testing tools for navigational equipment under rolling— has been developed. The holographic prism is a miniature sample of photosensitive material, which contains a system of superimposed holographic gratings, and a laser the radiation of which passes through gratings to form a fan of diffracted beams. The fan in a prism based on a calcium fluoride (fluorite) crystal with color centers contained six out-of-plane beams radiating from a region with a hard-to-localize center. This fact hindered calibration of the measure and its application in the testing device. The use of photothermo-refractive glass as a material for preparing a sample and recording a system of holograms in it makes it possible to eliminate the drawbacks of fluorite-based prism. The number of holograms rises up to 21, the fan becomes in-plane, and its center is localized in a small region, with a size of several tenths of the sample thickness (1–2 mm). The fan beams are energetically homogeneous, and each can be identified when using the fan in a testing device.     

Dispersion transition and the nonergodicity of the disordered nanoporous medium-nonwetting liquid system

The experiments in which a nonwetting liquid does not flow from a disordered nanoporous medium are described. The outflow is shown to depend on the degree of filling of the porous medium and its temperature in a critical manner. A physical mechanism is proposed where the transition of a system of liquid nanoclusters in a confinement into a metastable state in narrow filling and temperature ranges results from the appearance of a potential barrier due to the fluctuations of the collective “multiparticle” interaction of liquid nanoclusters in neighboring pores of different sizes at the shell of a percolation cluster of filled pores. The energy of a metastable state forms a potential relief with numerous maxima and minima in the space of a porous medium. The dispersed liquid volume in a metastable state is calculated with an analytical percolation theory for a ground state with an infinite percolation cluster. The outflow time distribution function of pores is calculated, and a power law is obtained for the decrease in nonwetting liquid volume retained in a porous medium with increasing time. The relaxation of the system under study is a multistage process accompanied by discontinuous equilibrium and overcoming of numerous local maxima of a potential relief. The formation of the metastable state of retained nonwetting liquid results from the nonergodicity properties of a disordered porous medium. The proposed model can describe the detected dependences of dispersed liquid volume on the degree of filling and temperature.     

Phase transitions in a few-electron quantum dot in a magnetic field: Wigner phases and broken-symmetry spin-singlet states

We develop a variational many-body approach within a second quantized formulation for a few-electron system in a parabolic two-dimensional quantum dot (QD). By way of application, the nature of the ground state of a two-electron system in a parabolic QD in a broad range of magnetic fields is theoretically investigated. Various phase transitions on the basis of the resulting analytical expressions for energy of the system have been investigated: First, the well-known transition from a maximum density droplet to a Wigner phase in a magnetic field is obtained, provided that the QD is in conditions of weak confinement. Furthermore, in the case of relatively strong QD confinement and weak magnetic fields, a rotationally symmetric spin-singlet state is the ground state of the system. However, in a strong magnetic field and for the same QD confinement, a broken-symmetry spin-singlet state appears to be energetically favored over the symmetric spin-singlet state. A first investigation of such a broken-symmetry spin-singlet phase in a QD in a magnetic field is shown to be an important application of the proposed technique. The text was submitted by the authors in English.     

氮化铝薄膜中的二次谐波产生

利用X射线衍射技术对用直流反应磁控溅射技术沉积在蓝宝石基底(100)晶面上的氮化铝(AIN)薄膜进行了晶体结构分析,对X射线衍射图样的分析结果表明：用该法沉积在蓝宝石基底(100)晶面上的AIN薄膜为单晶膜;利用脉宽为10ns、重复频率10Hz、最大平均功率为20W、单脉冲的最大能量为2J的Nd：YAG脉冲激光器对其进行了二次谐波产生的实验研究,对实验结果进行分析表明：沉积在蓝宝石基底(100)晶面上的AIN薄膜能在一个很宽的入射角度范围存在有效二次谐波的输出;且输出的二次谐波功率相对于AIN薄膜的表面法线成对称分布,这表明该AIN薄膜的表面法线方向即为AIN的光轴方向。     

The Klein-Gordon and the Dirac Oscillators in a Noncommutative Space

We study the Dirac and the Klein-Gordon oscillators in a noncommutative space. It is shown that the Klein-Gordon oscillator in a noncommutative space has a similar behaviour to the dynamics of a particle in a commutative space and in a constant magnetic field. The Dirac oscillator in a noncommutative space has a similar equation to the equation of motion for a relativistic fermion in a commutative space and in a magnetic field, however a new exotic term appears, which implies that a charged fermion in a noncommutative space has an electric dipole moment.     

Unidirectional Single-Mode 532-nm Nd:YAG Laser Using Intracavity Frequency Doubling in Nonplanar Ring Geometry

Intracavity frequency doubling of a single-mode Nd:YAG laser using a nonplanar ring cavity is demonstrated. The nonplanar ring cavity consists of a Brewster-angled Nd: YAG crystal placed in a magnetic field, a KTP crystal, and two spherical mirrors. In this design the Nd:YAG crystal acts as both a nonreciprocal polarization rotator and a partial polarizer, and the nonplanar portion of the ring cavity, which is formed by a relative twist angle between the Brewster-angled end surfaces of the crystal, serves as a reciprocal polarization rotator. Eigenpolarization theory for the cavity configuration is presented and a suitable value of the relative twist angle for unidirectional operation is estimated. A single-mode output power of 22 mW at 532 nm is obtained with a 1.2-W diode laser at 809 nm and a laser linewidth of less than 100 kHz is inferred from a beat note frequency spectrum between two identical laser systems.     

Solitons in a linear lattice with defects

Solitons are generated in an anharmonic linear lattice in which neighbouring atoms interact through a Morse potential by giving either a strong initial impulse or a large displacement to an end atom. Studies on the variation of the characteristic properties of the soliton with the strength of the initial pulse show that the velocity and the amplitude of the soliton increase with the strength of the initial impulse, but below a certain critical value for the initial impulse, only an oscillatory tail is generated. It is shown that when a defect is present in the lattice, a localised mode appears at the site of the defect and additional solitons travelling forward or even backwards, are generated. When two solitons collide at a defect region, they reemerge but leave a localised mode at the site of the defect. If an initial velocity is imparted to a particular particle, synchronously with the crossing of the particle by the soliton, a localised mode emerges at the site of the particle and additional solitons are also generated. When a soliton moves from a denser to a rarer medium, a strong localised pulse is created near the region of the density discontinuity and additional solitons appear; and further a weak oscillatory tail is left behind in the denser medium. On the other hand, if a soliton moves from a rarer to a denser medium, it is reflected back and a small localised mode is generated at the site of the density discontinuity. The variation of amplitude of the soliton with the velocity of propagation is also studied.     

Reorientation of a nonspherical capsule in creeping shear flow

The dynamics of a capsule and a biological cell is of great interest in chemical engineering and bioengineering. Although the dynamics of a rigid spheroid is well understood by Jeffery's theory, that of a spheroidal capsule remains unclear. In this Letter, the motion of a spheroidal capsule or a red blood cell in creeping shear flow is investigated. The results show that the orientation of a nonspherical capsule is variant under time reversal, though that of a rigid spheroid is invariant. Surprisingly, the alignment of a nonspherical capsule over a long time duration shows a transition depending on the shear rate, which can be utilized for a particle-alignment technique. These findings form a fundamental basis of the suspension mechanics of capsules and biological cells.     

Transition of a diffuse discharge to a spark at nanosecond breakdown of high-pressure nitrogen and air in a nonuniform electric field

The transition of a runaway-electron-induced diffuse discharge initiated in a nonuniform electric field under a high pressure of air and nitrogen to a spark is studied. High-voltage pulses with a rise time of 0.5 ns are applied to a discharge gap with a tubular cathode having a small radius of curvature. It is shown that the leader of the spark discharge propagates toward the tubular cathode along preproduced tracks and may pass from one track to another. For a pulse rise time of about 0.5 ns and a gap length of 12 mm or more, it is found that spark leaders originating at the cathode (which has a small radius of curvature) do not reach the anode and accordingly, do not cause the spark breakdown of the gap. It is confirmed that the spark breakdown of the gap is associated with a spark leader that moves away from the plane electrode after the appearance of a bright spot on it.     

Self-assembly of charged CdTe nanoparticles

We show a method of the organization of charged CdTe nanoparticles which allows the generation of a self-assembled monolayer of above 10.000 μm² in a time of about 90 s. The analysis of adsorption kinetics of particles on a surface shows that it is well described by the Langmuir isotherm. We have found that thermal and electrical conductivity of a substrate play an important role. Nevertheless, deficiency of a substrate does not affect the adsorption kinetic. The structure of a formed monolayer essentially depends on pH and, as a consequence, on the charge of the particles. This method can be effective for the production of a CdTe nanoparticle monolayer with well controlled area and a degree of filling on a surface.     

A wire trap for neutral atoms

We present new ways of trapping a neutral atom with static electric and magnetic fields. We discuss the interaction of a neutral atom with the magnetic field of a current carrying wire and the electric field of a charged wire. Atoms can be trapped by the 1/r magnetic field of a current-carrying wire in a two-dimensional trap. The atoms move in Kepler-like orbits around the wire and angular momentum prevents them from being absorbed at the wire. Trapping was demonstrated in an experiment by guiding atoms along a 1 m long current-carrying wire. Stable traps using the interaction of a polarizable atom with the electric field of a charged wire alone are not possible because of the 1/r ² form of the interaction potential. Nevertheless, we show that one can build a microscopic trap with a combination of a magnetic field generated by a current in a straight wire and the static electric field generated by a concentric charged ring which provides the longitudinal confinement. In all of these traps, the neutral atoms are trapped in a region of maximal field, in theirhigh-field seeking state.Dedicated to H. Walther on the occasion of his 60th birthday     

Strange pattern formation in a model for ferromagnetic resonance instability

The pattern formation process in a transversal circular pumped ferromagnetic resonance system above the second order Suhl instability is studied in a model which is a spatially one-dimensional partial integro-differential equation of motion with a periodic boundary condition. Instead of a bifurcation into a spatially periodic pattern, the homogeneous state bifurcates into a solution with a fast spatial oscillation which is modulated by a slow oscillation. Only for higher pumpfields a second bifurcation into a simple periodic state occurs.This work was performed within the program of the Sonderforschungsbereich 65 Darmstadt-Frankfurt     

On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions

This work is a continuation of the authors efforts to develop high-order numerical methods for solving elliptic problems with complex boundaries using a fictitious domain approach. In a previous paper, a new method was proposed, based on the use of smooth forcing functions with identical shapes, mutually disjoint supports inside the fictitious domain and whose amplitudes play the role of Lagrange multipliers in relation to a discrete set of boundary constraints. For one-dimensional elliptic problems, this method shows spectral accuracy but its implementation in two dimensions seems to be limited to a fourth-order algebraic convergence rate. In this paper, a spectrally accurate formulation is presented for multi-dimensional applications. Instead of being specified locally, the forcing function is defined as a convolution of a mollifier (smooth bump function) and a Lagrange multiplier function (the amplitude of the bump). The multiplier function is then approximated by Fourier series. Using a Fourier Galerkin approximation, the spectral accuracy is demonstrated on a two-dimensional Laplacian problem and on a Stokes flow around a periodic array of cylinders. In the latter, the numerical solution achieves the same high-order accuracy as a Stokes eigenfunction expansion and is much more accurate than the solution obtained with a classical third order finite element approximation using the same number of degrees of freedom.