Vibrations of double-string complex system under moving forces. Closed solutions

In this paper the dynamic response of a double-string system traversed by a constant or a harmonically oscillating moving force is considered. The force is moving with a constant velocity on the top string. The strings are identical, parallel, one upon the other and continuously coupled by a linear Winkler elastic element. The classical solution of the response of a double-string system subjected to a force moving with a constant velocity has a form of an infinite series. The main goal of this paper is to show that in the considered case a part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method of finding the solution in a closed, analytical form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations.     

Physical adsorption and surface plasmons

The quantum mechanical formulation of the screening of a point charge by surface plasmons is extended to describe the coupling of a fluctuating atomic dipole with a metallic surface of planar, spherical or cylindrical shape. This allows for the calculation of the nonretarded Van der Waals attraction of an atom by a solid surface in the three different geometries. Applications of the theoretical formulae are made to obtain numerical values of the dispersion energy by a spherical particle, a spherical pore, a thin film, a slot-like prore, a cylindrical fiber or a cylindrical pore.     

On reconstructing photon statistics by on/off detectors: Toward the multi-partite case

The propagation of pulses of the pump and its second harmonic in a quadratically nonlinear medium whose linear properties are characterized by a negative refractive index at the pump frequency and by a positive refractive index at the harmonic frequency is considered theoretically. In the case of a low intensity of the interacting waves, the pump and second-harmonic pulses propagate in the opposite directions, but sufficiently powerful pulses can form a simulton—a solitary two-frequency wave propagating in a certain direction as a single whole. Solutions to a set of equations are found which describe the steady-state propagation of a solitary wave and of a nonlinear periodic (cnoidal) wave.     

Interaction of electromagnetic waves with nonlinear substance layer under conditions of electron paramagnetic resonance in millimeter waves

Trancated equations have been obtained by the Green's functions method for a slowly varying amplitude of a transverse magnetic field component in a paramagnetic layer under conditions of the electron paramagnetic resonance (EPR). A magnetic susceptibiliti of the substence has been found from the Bloch equation for a homogeneously line breadth of the EPR. In a stationary case a solution of a nonlinear boundary-value problem is redused to a solution of two boundary problems for amplitude and phase equations. It is shown that unstable regimes of the electrodynamic system under inves tigation are possible.Electrodynamic characteristics of a nonlinear resonator of the Fabry-Pero type filled with a saturated paramagnetic medium have been analyzed numerically in a non-stationery case.     

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.     

Measuring Light Field of Light Source with High Directional Resolution Using Mirrored Ball and Pinhole Camera

This paper presents a method of measuring a light field of a light source with high directional resolution using a mirrored ball and a pinhole camera. The light field describes a spatial and directional distribution of radiances from the light source. The directional distribution is expanded by a reflection on the mirrored ball, and the radiances are measured by a charge-coupled device (CCD) camera with a pinhole lens. The light source is laterally moved by a robot arm to measure the directionally expanded light field, and each pixel on a CCD can obtain the radiances from the light source through the pinhole lens with high directional resolution. The light field is estimated from the pixel value and the position of each pixel using a ray tracing technique. The light field of a krypton lamp was experimentally measured by the proposed method, and the accuracy of the measurement was evaluated against the irradiances measured by a spectro-radiometer at sample points.     

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.     

Reconstruction of the acoustic impedance profile in a plate using an inverse spectral procedure

An inverse spectral procedure was applied to reconstruct the acoustic impedance profile along the thickness direction of a plate using its thickness resonance frequencies, density and thickness. For a successful reconstruction, the material-property profile must be symmetric about the mid-plane of the plate. Several cases of numerical simulations, including plates with a few layers and with a high number of layers are described. The calculated resonance frequencies were used to reconstruct the acoustic impedance profile, a process that was successful for all cases. We assume that a plate with a high number of layers, each with a different but constant acoustic impedance, simulates a plate with a smoothly varying acoustic impedance profile. It can be concluded that such a plate, which generates small, virtually undetectable, internally reflected waves, can also be reconstructed. In the special case of a plate of unknown thickness and unknown but constant density, the method is still useful, because a relative variation of the material property can be reconstructed using only the resonance frequencies. An experiment using a resonance-mode electromagnetic acoustic transducer (resonance-mode EMAT) is also described. EMAT is a non-contact ultrasonic method that can measure thickness resonance frequencies, making it appropriate for this method. Some examples of applications are measurement of the temperature profile inside a rolled metal sheet, measurement of a clad metal plate, and monitoring of a metal casting.     

Weak values of electron spin in a double quantum dot

We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device. The weak value is obtained by a two step procedure--weak measurement followed by a strong one (postselection), where the outcome of the first measurement is kept provided a second postselected outcome occurs. The setup consists of a double quantum dot and a weakly coupled quantum point contact to be used as a detector. Anomalously large values of the spin of a two electron system are predicted, as well as negative values of the total spin. We also show how to incorporate the adverse effect of decoherence into this procedure.     

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.     

Speckle-pattern rotation in a few-mode optical fiber in a longitudinal magnetic field

The process of rotation of a speckle pattern at the output of a few-mode optical fiber in a longitudinal magnetic field is mathematically modeled. It is shown that the deviation from a linear relation between the rotation angle of a speckle pattern at the output of a few-mode fiber and the fiber length in the presence of a longitudinal magnetic field results from a specific dependence of polarization corrections to the propagation constants of TE and TM modes. The calculation results are compared with the results of an experiment on determining the rotation angle of a speckle pattern as a function of magnetic field in a fiber of constant length.     

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.     

Boundary crisis and transient in a dissipative relativistic standard map

Some dynamical properties for a problem concerning the acceleration of particles in a wave packet are studied. The model is described in terms of a two-dimensional nonlinear map obtained from a Hamiltonian which describes the motion of a relativistic standard map. The phase space is mixed in the sense that there are regular and chaotic regions coexisting. When dissipation is introduced, the property of area preservation is broken and attractors emerge. We have shown that a tiny increase of the dissipation causes a change in the phase space. A chaotic attractor as well as its basin of attraction are destroyed thereby leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with the stable manifold of a saddle fixed point. Once the chaotic attractor is destroyed, a chaotic transient described by a power law with exponent −1 is observed.     

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.     

Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.     

具有态守恒赝隙的光子晶体中两能级原子自发辐射的增强与抑制

论证了在赝带隙光子晶体中存在一个全频率域态总数守恒规则，在完全带隙光子晶体中还存在一个局域态总数守恒规则.态总数守恒规则指出，如果一个光子晶体的态密度在某些频率范围存在相对于等效介质态密度的谷，则一定由其他频率范围内相对于等效介质态密度的峰来补偿.使用符合态总数守恒规则的态密度模型，解释了态密度调制导致的自发辐射谱增强、抑制、变窄、红移、蓝移以及谱分裂等光子晶体中的量子光学现象.该理论比较适合研究在具有赝带隙的光子晶体中大量随机分布的发光原子或分子的自发辐射行为. 关键词： 光子晶体 自发辐射 态密度 光子赝带隙     

Soliton matter and the onset of color conductivity

We employ the hybrid soliton model of the nucleon consisting of a topological meson field and deeply bound quarks to investigate the behavior of the quarks on soliton matter as a function of density. We investigate a particular possible ground state by placing the solitons on a spatial lattice. The model suggests the transition of matter from a color insulator to a color conductor above a critical density of a few times normal nuclear density.