Solving a relativistic quasipotential equation for a superposition of a nonlocal separable and a local quasipotential

Within the relativistic quasipotential approach to quantum field theory, a method is developed for solving a finite-difference quasipotential equation for the case where a total quasipotential describing the interaction of two relativistic spinless particles of unequal masses is a superposition of a nonlocal separable and a local quasipotential. The cases are investigated where the local component of the total interaction—it is assumed to be known—either admits or does not admit the existence of bound states. This makes it possible to obtain an exact expression for the increment of the phase shift, to determine the conditions of the existence of bound states, and to give a generalization of the Levinson theorem.     

Tunnelling process between a semiconductor or a metal and a polymer

The tunnelling lifetime of an electron lying in a p-type orbital localised at a given distance from a semiconductor or a metal is calculated by using Bardeen's method. It is then shown that even in the absence of broad bands, the hole injection process from semiconductors and metals into polymers should follow a Fowler-Nordheim dependence, provided that the current is not bulk-limited. In the semiconductor case, the current can be expressed by a fully analytical formula, and by an approximate one in the case of a metal. It is demonstrated that the effective Fowler-Nordheim barrier is not the mere difference between the metal work function or the semiconductor electron affinity and the HOMO level of the polymer, but a simple function of both levels. Received 6 April 2001 and Received in final form 29 May 2001     

Modeling a waveguide with a nonlinear insert with a quadratic nonlinearity

The scalar problem of the scattering of a wave from a nonlinear insertion lying in the interior of a waveguide is reduced by the incomplete Galerkin method to the boundary value problem for a Hamiltonian system. The cases in which this problem admits a solution in finite terms are indicated. Examples are given to illustrate specific phenomena due to the nonlinearity of the problem.     

Formation of a bistructure of a solid in a computer experiment

Molecular-dynamics was used to investigate the structural changes occurring in a three-dimensional solid when the solid is transferred from an amorphous into a crystalline state. Crystal cells of a new type — pentadecahedrons with five square lateral faces and ten regular triangular faces at the vertices of a cell — were found for the first time in a computer experiment. It is shown that a bistructure consisting of crystal cells of different types, including cells with five-fold symmetry axes, are stable in the solid. Fiz. Tverd. Tela (St. Petersburg) 40, 1919–1924 (October 1998)     

Parastatistics and phase transition from a cluster as a fluctuation to a cluster as a distinguishable object

A phase transition of the first kind is a jump of a function, a phase transition of the second kind is a jump of its first derivative, a phase transition of the third kind, a jump of the second derivative. A phase transition from one statistic to another is very gradual, but finally it is as considerable as the phase transition of the first kind. However, we cannot introduce a clearly defined parameter to which this transition corresponds. This is due to the fact that the fluctuations near the critical point are huge, and this violates, in the vicinity of that point, the main law of equilibrium thermodynamics, which asserts that fluctuations are relatively small. The paper describes the transition in the supercritical fluid region of equilibrium thermodynamics from parastatistics to mixed statistics, in which the Boltzmann statistics is realized for long-living clusters. In economics this corresponds to a negative nominal credit rate. Examples of this non-standard situation are presented.     

Diffraction of a Bose-Einstein condensate from a magnetic lattice on a microchip

We experimentally study the diffraction of a Bose-Einstein condensate from a magnetic lattice, realized by a set of 372 parallel gold conductors which are microfabricated on a silicon substrate. The conductors generate a periodic potential for the atoms with a lattice constant of 4 microm. After exposing the condensate to the lattice for several milliseconds we observe diffraction up to fifth order by standard time of flight imaging techniques. The experimental data can be quantitatively interpreted with a simple phase imprinting model. The demonstrated diffraction grating offers promising perspectives for the construction of an integrated atom interferometer.     

Surface polaritons in a dielectric at a boundary with a metal in a static electric field

The existence of surface polaritons in a dielectric at a boundary with an ideal metal or superconductor in a static electric field is predicted. The frequency regions in which polaritons exist are substantially different for opposite orientations of the electric field, so that a change in the direction of the field signifies “switching on” or “switching off” of surface polaritons with a fixed frequency. Pis'ma Zh. éksp. Teor. Fiz. 68, No. 12, 876–880 (25 December 1998)     

Solution of a cauchy problem for a diffusion equation in a Hilbert space by a Feynman formula

The Cauchy problem for a class of diffusion equations in a Hilbert space is studied. It is proved that the Cauchy problem in well posed in the class of uniform limits of infinitely smooth bounded cylindrical functions on the Hilbert space, and the solution is presented in the form of the so-called Feynman formula, i.e., a limit of multiple integrals against a gaussian measure as the multiplicity tends to infinity. It is also proved that the solution of the Cauchy problem depends continuously on the diffusion coefficient. A process reducing an approximate solution of an infinite-dimensional diffusion equation to finding a multiple integral of a real function of finitely many real variables is indicated.     

Cavitation in a lubrication flow between a moving sphere and a boundary

A heavy sphere is free to move inside a rotating horizontal cylinder filled with viscous liquid. The steady motion is essentially Stokesian, and the sphere rotates at a fixed location with a lubrication layer between the ball and the wall. The symmetry of the flow field suggests there will be no force to balance the normal component of the ball's weight. However, we show that a normal force can arise when a cavitation bubble is present. The bubble size was measured as a function of the cylinder rotation rate and agrees well with a model which uses the force and torque balances on the sphere.     

Pancharatnam phase for a system of a two-level atom interacting with a quantized field in a cavity

We derive an expression for the Pancharatnam phase for the entangled state of a single two-level atom interacting with a single electromagnetic field mode in an ideal cavity with the atom undergoing either a one- or a two-photon transition. It is shown that the Pancharatnam phase explicitly contains information about the statistics of the field and atomic coherence.     

Spectrum of a particle on a polyhedron enclosing a synthetic magnetic monopole

We consider a single particle hopping on a tight binding lattice formed by the vertices of a regular polyhedron and discuss the effect of a magnetic monopole enclosed in the polyhedron. The presence of the monopole induces phases on the hopping terms, given by Peierls substitution. By requiring the flux through each face of a regular polyhedron to be the same, Dirac’s quantization condition is obtained in this discrete setting. For each regular polyhedron, we calculate the energy spectrum for an arbitrary value of the flux through a Dirac string coming in from one of the faces. We find that the energy levels are degenerate only when the flux through the Dirac string corresponds to a quantized monopole. We show that the degeneracies in the presence of the monopole can be classified using the double group of the symmetry of the polyhedron and label all energy levels with corresponding irreducible representations.     

Rigorous solution of a problem for a cylindrical cavity containing a ferrite

Conclusions Equation (6) relates the complex frequency for a TM_nmo mode in a cylindrical cavity to the geometrical parameters, ferrite parameters, and volume and position of the specimen.Formula (6) is a generalization of characteristic equations previously derived [3, 4], which are of great value.The dispersion equation of (6) is of interest in that it allows one to calculate the effects of the dielectric parameters on the cavity, which is of value if a large tuning range is needed.Numerical results are rather laborious to obtain, but some valuable conclusions can be drawn in a relatively simple fashion, as will be shown in a forthcoming paper.     

Application of a reflector with a nonuniform field in a mass-reflectron

The conditions under which the nonuniform compensating field of the reflector of the mass-reflectron can be generated with an acceptable accuracy at the symmetry axis of the reflector and extrapolated to the radial neighborhood of the axial line are determined. The plots that illustrate the distribution of the calculated nonuniform field of the reflector, the possibilities for implementation, and errors of focusing with respect to time of flight in the radial neighborhood are presented. Analytical expressions for the calculation of the time of flight of ions in the reflector in which the field distribution is described using a power series and analytical expressions for the calculation of the field distribution in the reflector in which the time of flight is determined using a power series are derived. A method for the analytical calculation of the compensating nonuniform field of the reflector based on the given dependence of the time of flight in the absence of such a field is proposed using a solution to the Abel integral equation. The solution to this equation yields analytical expressions for the calculation of the compensating field of the reflector in mass-reflectrons that contain the zero-field drift space and regions of acceleration (deceleration) of ions with a uniform field.     

Instability of a flat horizontal interface between a thin layer of a ferrofluid and a thin layer of a nonmagnetic liquid in the presence of a vertical magnetic field

An asymptotic analysis of the equations and boundary conditions of fluid dynamics is performed, and a nonlinear model is constructed for the onset of the development of Rosensweig instability in a thin horizontal ferrofluid layer at rest covered with a thin layer of a lighter nonmagnetic liquid. The surface of a nonmagnetized slab is the lower boundary of the ferrofluid, and the interface with a gas is the upper boundary of the nonmagnetic liquid. The pressure in the gas is constant. The instability being considered arises upon the application of a rather strong uniform vertical magnetic field. The proposed model involves five dimensionless parameters. The critical magnetization of the initial ferrofluid layer with a flat upper boundary and the threshold wave number are found. The effect of the governing parameters on the instability region and on the wavelength of the fastest growing mode is studied in the linear formulation of the problem.     

Admittance of a groove on a rigid surface under a grazing flow

The problem of sound diffraction by a groove on a rigid surface in the presence of a grazing flow is considered. The input admittance of the groove is calculated, and its real part is shown to be negative.     

Resolution enhancement at a large convergence angle by a delta corrector with a CFEG in a low-accelerating-voltage STEM

Resolution reduction by a diffraction limit becomes severe with an increase in the wavelength of an electron at a relatively low accelerating voltage. For maintaining atomic resolution at a low accelerating voltage, a larger convergence angle with aberration correction is required. The developed aberration corrector, which compensates for higher-order aberration, can expand the uniform phase angle. Sub-angstrom imaging of a Ge [1 1 2] specimen with a narrow energy spread obtained by a cold field emission gun at 60 kV was performed using the aberration corrector. We achieved a resolution of 82 pm for a Ge–Ge dumbbell structure image by high angle annular dark-field imaging.     

Reflection of a surface mode from a break in a dielectric waveguide

The problem of surface mode reflection from a break in a dielectric waveguide of arbitrary cross section is solved by a variational method. The dependences of the reflection coefficient on the size and cross-sectional shape of the waveguide are examined. Comparisons with results obtained by other methods, including the data calculated for the 2-D problem (a break in a dielectric plate), are presented. P. L. Kapitsa Institute of Physical Problems, Russian Academy of Sciences, Moscow, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 8, pp. 1004–1018, August, 1997.     

Arbitrary tensor concomitants of a bivector and a metric in a space-time manifold

In the general theory of relativity the energy-momentum tensor due to an electromagnetic field is taken to be a symmetric rank-two tensor concomitant of a bivector and the metric tensor. As a step in the discussion of the possible uniqueness of this tensor we display a method for finding all tensor concomitants of a bivector and a metric in a space-time manifold.