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.     

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     

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.     

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.     

Nanoscale hydrodynamic instability in a molten thin gold film induced by femtosecond laser ablation

A mechanism of the formation of a nanotip with a nanoparticle at its top that appears in a thin metal film irradiated by a single femtosecond laser pulse has been studied experimentally and theoretically. It has been found that the nanotip appears owing to a melt flow and a nanojet formation, which is cooled and solidified. Within a proposed hydrodynamic model, the development of thermocapillary instability in the melted film is treated with the use of the Kuramoto-Sivashinsky-type hydrodynamic equation. The simulation shows that the nanojet nucleates in the form of a nanopeak in a pit on the top of a microbump (linear stage) and, then, grows in a nonlinear (explosive) regime of an increase in thermocapillary instability in good agreement with experimental data.     

Settling Behavior Characterization of Submicron Particles in Dilute and Concentrated Suspensions

In separation processes, the knowledge of particle size and density arc often not enough to describe the settling behaviour in a concentrated suspension. Therefore, a direct method for the characterization of the settling behavior of submicron particles in concentrated suspensions is introduced in a centrifugal field by a manometric sedimentation analysis. By means of this cumulative method in a homogeneous suspension, the analyses of both the interfacial settling rate and the settling rate of the particles within the concentrated suspension are possible. This permits a differential examination of settling processes in a broad concentration range. First, the influence of the solid concentration on the settling rate at the interface and within a monodisperse suspension with a range from 0.01 to 30 vol.% is represented. The relationship between the increase in settling rate through particles settling in a cluster and a concentration decrease in the suspension is also represented. Consideration of the possibilities of the analysis of polydisperse suspensions demonstrates the field of applications for this method.     

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.     

Analytical formula for a decentered elliptical Gaussian beam propagating in a turbulent atmosphere

Analytical formulas for the average intensity and decentered parameter of a decentered elliptical Gaussian beam (DEGB) propagating in a turbulent atmosphere are derived in a tensor form. The propagation properties of a DEGB in a turbulent atmosphere are investigated in detail, and found to be different from that in free space. Furthermore, as an application example, we investigate the propagation of a decentered elliptical flat-topped beam (DEFB) by expressing its electric field as a finite sum of DEGBs in a turbulent atmosphere. The properties of a DEGB or a DEFB in a turbulent atmosphere are closely related with the beam’s parameters and the structure constant of the turbulent atmosphere.     

Dynamic reflection and refraction of neutrons at the boundaries of matter characterized by a variable magnetic induction

Optical phenomena that arise in the interaction of a neutron wave with matter characterized by a variable interaction potential are considered. The time dependence of the potential is assumed to be due to a change in the magnetization vector in matter with time. Since the interaction in question is time-dependent, the neutron energy is not conserved. If a neutron interacts with a sample that has a plane boundary, only the neutron-velocity component orthogonal to the matter boundary changes. Thus, reflected waves are characterized by a reflection angle that is different from the angle of incidence. Waves transmitted through a plane sample can also change direction. The changes in the neutron energy and in the neutron-velocity direction are closely related to the reversal of the neutron-spin projection. The question of whether a slab featuring a rotating magnetization vector can be used as a spin flipper or as a coherent wave splitter is considered.     

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.     

Radial motion of a solid spherical body in a magnetic field

The object of the present paper is to investigate the radial motion of a solid spherical body, assumed to be homogeneous, isotropic and elastic, in presence of a magnetic field in the azimuthal direction. The body is assumed to be in a state of initial stress which is hydrostatic in nature. This theory of radial motion of a solid spherical body in a magnetic field has been utilised to find the small radial motion of a solid Earth assumed to be homogeneous isotropic elastic sphere in presence of a magnetic field in the azimuthal direction. Considering the effect of gravity and the initial stress produced by slow process of creep due to extra masses over the surface of the Earth, the fundamental equations of motion are derived which are non-linear in character and are solved. The times of a desired radial displacement are calculated in presence of a magnetic field only and in presence of the same magnetic field, initial stress and gravitational field, which are compared and exhibited numerically.     

Nonsteady waves in distributed dynamical systems

The paper is devoted to the study of one-dimensional and two-dimensional transient wave regimes in nonlinear systems of the reaction-diffusion type. In a one-dimensional case the process of collision of two travelling waves is considered. It is demonstrated that in the case of a nondispersive nonlinear system, where a steady regime of the collision is not possible, the process can be described by means of an approximation which is nonuniform in a spatial coordinate. The collision results, in a general case, in formation of an oscillatory shock wave moving with varying velocity. In a two-dimensional situation the transition of a rotating vortex into a rotating spiral wave in the case of dispersive systems and the inverse transition in the case of nondispersive systems are considered.     

Measurement of the parameters of the natural waveguide mode

The possibilities of using the decomposition of natural waveguide modes in a shallow-water sea in case there is a sound velocity gradient into sinusoidal modes of an ideal waveguide is grounded. The applicability range of such decomposition is shown. Dispersion in signals of the modes presented in such a way is determined by mathematical reversal without a test source. The structure of discrete modes in a natural waveguide is determined without utilizing the bottom parameters and sound velocity’s distribution over the waveguide depth. The coefficient of the mode signal’s correlation with the measured parameters of the mode signal and a real signal, introduced into it, is shown to be 0.973. The signals from a point emitter positioned at the depth of 50 m in the frequency range of 90–280 Hz in a shallow-water sea (the Barents Sea, a 120 m depth, a 7 km distance), received by a vertical antenna array comprising 32 receivers spaced equidistantly with a 3-m step are used in the experiment. A real signal has been successfully reversed using a mathematical model.     

The Wigner crystal in a semimetal film in a high magnetic field

The possibility of existance of a super-crystalline (Wigner) phase in a semimetal or impurity semiconductor film placed in a high magnetic field, is discussed and a comparison is made with a crystal in a three-dimensional specimen.

Such a phase exists in a succession of magnetic field or particle density intervals. The vibrational spectrum depends on magnetic field, while the bind energy is only density-dependent. The mean-square displacement x² of the particles in the lattice sites are also independent on the magnetic field over a wide temperature range.     

Gravitational coupling and dynamical reduction of the cosmological constant

We introduce a dynamical model to reduce a large cosmological constant to a sufficiently small value. The basic ingredient in this model is a distinction which has been made between the two unit systems used in cosmology and particle physics. We have used a conformal invariant gravitational model to define a particular conformal frame in terms of large scale properties of the universe. It is then argued that the contributions of mass scales in particle physics to the vacuum energy density should be considered in a different conformal frame. In this manner, a decaying mechanism is presented in which the conformal factor appears as a dynamical field and plays a key role to relax a large effective cosmological constant. Moreover, we argue that this model also provides a possible explanation for the coincidence problem.     

Probabilistic radiative transfer—Two simply coupled spectral lines

The diffusion of radiation in a pair of coupled spectral lines formed by electron transitions between two excited levels and a common lower level is formulated in terms of probability functions for the case of a plane-parallel atmosphere. The equations are solved numerically for the four distributions with depth in the atmosphere for the probability that a photon formed in a specified line at a particular depth eventually escapes in a specified line. The behavior of the solutions is interpreted on the basis of simple probability models. An equation expressing the difference in the source functions of the lines in terms of the probability functions is derived and discussed.     

Effect of irradiation with Ne<Superscript>+</Superscript> ions on the transformations of domain structures of a uniaxial magnetic film in an AC magnetic field

Effects of irradiation with Ne⁺ ions on the transformations of domain structures (DSs) that occur in a uniaxial magnetic film under the action of an ac magnetic field are investigated. Transitions of a DS from an amorphous state into a hexagonal lattice and a labyrinthine structure are considered. The irradiation is found to lead to a change in the amplitudes of the ac field at which phase transformations of the DS occur. The effect of the magnitude of the ac field on the number of domains in a block with a hexagonal lattice has been studied. It is shown that the process of annealing of defects in a DS consisting of blocks with a hexagonal lattice can be described by the equation of a first-order reaction. The irradiation-induced change in the energy of activation for the annealing of defects in the DS has been found.     

Topological entanglement entropy

We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho) = alphaL - gamma + ..., where the ellipsis represents terms that vanish in the limit L --> infinity. We show that - gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium.     

Methyl orbital signatures in 2-amino-1-propanol

Electron density distributions of 2-aminoethanol (2AE) and 2-amino-1-propanol (2AP) are calculated in both the coordinate and the momentum spaces using the B3LYP/TZVP method. Using the dual space analysis, molecular orbital signatures of the methyl substituent in 2AP are identified with respect to 2AE. Relaxations of the geometry and the valence orbital in 2AP are found to be due to the insertion of the methyl group. Five orbitals, not four orbitals, are identified as the methyl signatures. They are orbital 5a in the core shell, orbitals 9a and 10a in the inner valence shell, and orbitals 15a and 16a in the outer valence. In the inner valence shell, the attachment of methyl to 2AE causes a splitting of its orbital 8a into orbitals 9a and 10a of 2AP, whereas in the outer valence shell, the methyl group results in the insertion of an additional orbital pair of 15a and 16a. The frontier molecular orbitals 21a, 20a, and 19a are found to have no significant role in the methylation of 2AE.     

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 ofa 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.