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.     

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.     

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.     

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.     

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.     

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.     

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.     

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     

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.     

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.     

Localized States of an Excess Electron in an Ionic Cluster

A theory of an electron affinity for an ionic cluster is proposed both in a quasiclassical approach and with quantization of a polarization electric field in a nanoparticle. A critical size of the cluster regarding in formation of an electron's autolocalized state, dependencies of energy and radius of a polaron on a cluster's size are obtained by a variational method. It has been found that binding energy of the electron in the cluster depends on a cluster's radius but a radius of electron's auto-localization does not depend on the cluster's radius and it equals to the polaron radius in a corresponding infinity crystal. A bound state of the electron in a cluster is possible only if the cluster's radius is more than the polaron radius.     

Discrimination of fundamental frequency of synthesized vowel sounds in a noise background

An experiment was carried out, investigating the relationship between the just noticeable difference of fundamental frequency (jndfo) of three stationary synthesized vowel sounds in noise and the signal-to-noise ratio. To this end the S/N ratios were measured at which listeners could just discriminate a series of changes in fo in the range from 10% to 0.5%. Similar measurements were obtained for pulse trains and for pure tones as a reference for the results. A measure of S/N ratio based on an approximation of the critical bandwidth appeared to provide a fairly good predictor of the masked threshold of each signal, measured in a second experiment. Using this measure, it was found that a given change in the fundamental of a pulse train could be discriminated at a lower S/N ratio than in a pure tone with a frequency equal to that fundamental. The results for the vowel sounds were found to be in between those for a low-frequency pure tone and those for a pulse train. Owing to the signal-generation method (viz., changing fo by changing the sampling frequency), three cues could in principle be used to discriminate a change in the fundamental of a vowel: A change in the residue pitch, a change in the pitch of a single prominent harmonic, or a change in the spectral envelope of the signal. It can be inferred from the results that the subjects used that particular cue which yielded best performance. Which cue was optimal depended not only on the vowel but also on fo and on the presented change in fo.(ABSTRACT TRUNCATED AT 250 WORDS)     

Some laws of polarization and dispersion of a drop in an electrostatic field

The laws of distribution among contributions in various interactions to the total polarization energy of a conductor in a uniform electrostatic field was analyzed. It is shown that in a closed system, spontaneous shape variations of a liquid conductor with a free surface in an external magnetic field are possible only if they are accompanied by an increase in the conductor dipole moment. Variations of the intrinsic energy of a conductor are studied by the example of a conductive liquid drop in the case where a drop affected by a polarization charge becomes unstable. Analytical expressions defining the sizes and charges of the droplets ejected out of the initial drop under the conditions of instability are derived.     

Modulation instability of electromagnetic excitations in nonlocal Josephson electrodynamics of thin films of nonmagnetic and magnetic (two-and three-dimensional) superconductors

Modulation instability of nonlinear electromagnetic excitations (oscillating with the Josephson frequency) of finite amplitude is investigated in a Josephson junction in a film of a nonmagnetic, as well as of a magnetic (two-or three-dimensional), superconductor. The instability is accompanied by a nonlinear shift in frequency. Dispersion relations are derived for the time increment of small perturbations of the amplitude. It is shown that, for this type of excitations in a Josephson junction in a thin film of nonmagnetic superconductor, modulation instability develops only in a certain finite range of wave vectors, whereas in a thin film of a two-or three-dimensional magnetic superconductor it develops for any wave vector.     

Collisionally induced transport in periodic potentials

We study the transport of ultracold atoms in a tight optical lattice. For identical fermions the system is insulating under an external force while for bosonic atoms it is conducting. This reflects the different collisional properties of the particles and reveals the role of interparticle collisions in establishing a macroscopic transport in a perfectly periodic potential. Also in the case of fermions we can induce a transport by creating a collisional regime through the addition of bosons. We investigate the transport as a function of the collisional rate and observe a transition from a regime in which the mobility increases with increasing collisional rate to one in which it decreases. We compare our data with a theoretical model for electron transport in solids introduced by Esaki and Tsu.