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.     

Some non-abelian phase spaces in low dimensions

A non-abelian phase space, or a phase space of a Lie algebra, is a generalization of the usual (abelian) phase space of a vector space. It corresponds to a para-Kähler structure in geometry. Its structure can be interpreted in terms of left-symmetric algebras. In particular, a solution of an algebraic equation in a left-symmetric algebra which is an analogue of classical Yang–Baxter equation in a Lie algebra can induce a phase space. In this paper, we find that such phase spaces have a symplectically isomorphic property. We also give all such phase spaces in dimension 4 and some examples in dimension 6. These examples can be a guide for a further development.     

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.     

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.     

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.     

Magnon mechanism of defect reactions in solids

A phenomenological theory is developed that describes the effect of a magnetic field on the defect reactions in a solid. The theory is based on a concept regarding the lattice magnetism according to which a defect induces a magnetoactive (magnon) branch in the spectrum of elementary excitations of a crystal lacking a magnetic structure in the absence of defects. The probability of a defect complex disintegrating in a magnetic field is calculated in terms of the magnon mechanism of the reaction.     

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.     

矩形波导与圆柱波导或圆柱谐振腔间的小孔耦合

本文讨论了三种不同系统的小孔耦合的近似解法:矩形波导与圆柱波导的同轴耦合,矩形波导中的TE₁₀型波与圆柱谐振腔中的TM₁₂₀型波间的耦合和矩形波导中的TE₁₀型波与圆柱波导中的TM_mn型波间的耦合。通过这几个问题的解法,我们希望读者可以看到处理复杂微波元件问题时所需的从物理概念出发的灵活应用已有方法的必要性。这里提供的几个公式有着广泛的应用范围而是在现有文献中探讨得不够的。这里介绍的方法可以应用到其他新的微波网络问题中去。     

Spatial structure of a vortex in low density neutron matter

We study in a fully self-consistent approach the structure of a vortex in low density superfluid neutron matter. We determine that the matter density profile of a vortex shows a significant depletion in the region of the core, a feature never reported for a vortex state in a Fermi superfluid.     

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.     

Finite-size effect in shot noise in hopping conduction

We study a current shot noise in a macroscopic insulator based on a two-dimensional electron system in GaAs in a variable range hopping (VRH) regime. At low temperature and in a sufficiently depleted sample a shot noise close to a full Poissonian value is measured. This suggests an observation of a finite-size effect in shot noise in the VRH conduction and demonstrates a possibility of accurate quasiparticle charge measurements in the insulating regime.     

Signatures of resonance superfluidity in a quantum Fermi gas

We predict a direct and observable signature of the superfluid phase in a quantum Fermi gas, in a temperature regime already accessible in current experiments. We apply the theory of resonance superfluidity to a gas confined in a harmonic potential and demonstrate that a significant increase in density will be observed in the vicinity of the trap center.     

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.     

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.     

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.     

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.     

Investigation of a nonequilibrium polariton condensate in cylindrical micropillars in a strong magnetic field

We analyze the photoluminescence of a nonequilibrium polariton condensate in cylindrical micropillars etched on the surface of a high-Q GaAs microcavity in a wide range of detunings in a magnetic field up to 12 T for various levels of nonresonant laser pumping by nanosecond pulses. With such a method of excitation, a considerable effect of the interaction of the reservoir of photoexcited excitons with the condensate on the Zeeman splitting of the polariton condensate levels can be expected, which can lead to a decrease in its value and even to sign reversal. However, the measurements of photoluminescence in a wide range of optical excitation densities show that Zeeman splitting weakly depends on the optical pumping (its variation does not exceed 15% of the splitting in a field of 12 T). The estimation of the exciton density in the reservoir based on these data gives a value lower than 10⁸ cm^–2. In addition, a noticeable decrease (by a factor of about 1.8) in the polariton condensation threshold in a magnetic field is detected.