Diffraction of a Guided Mode of a Dielectric Waveguide

Using the finite-difference time-domain method, we solve the problem of diffraction of a guided mode of a planar dielectric waveguide by an arbitrary-shaped body. Particular results are obtained for the scatterers in the form of isolated circular and elliptic cylinders and metal strips. We calculate the reflection and transmission coefficients of the mode along with the field structure in the near zone. Comparison with the results obtained by expansion in terms of plane waves is performed for a test problem of diffraction of the mode by a circular metal cylinder.     

Binding energy of a screened donor in a spherical quantum dot with a parabolic potential

A wavefunction is proposed for calculating the ground-state energy of a screened donor in a spherical quantum dot under a parabolic potential by a variational method. The donor is taken to be at the center of the quantum dot. Results are presented for four values of the screening parameter by the proposed wavefunction as well as for the hydrogenic donor case by a wavefunction used by Xiao et al.. To assess the accuracy of the results, ‘exact’ energies are also obtained by numerical integration of the Schrödinger equation. It is shown that the proposed wavefunction gives very good results in all cases including the hydrogenic donor case.     

Dielectric alignment of a non-polar molecule substituting a polar molecule in a lattice of molecular dipoles

The dielectric alignment of a dilute non-polar component in a polar solvent may be determined by NMR spectroscopy. In this paper a series expansion of the alignment up to second order terms in the dipolar interaction is presented for a non-polar molecule replacing a single polar molecule in a rigid lattice of molecular dipoles. Assuming isotropic polarizabilities for all molecules Van Vleck earlier applied the lattice model in a theory of the dielectric constant of a dilute solution.In the present calculation the polarizabilities of the non-polar molecule and the dipoles are assumed to be anisotropic and isotropic, respectively. The anisotropy of the non-polar molecule is relevant, since the value of the alignment is zero for the isotropic case. Different results are obtained for cubic lattices and for a lattice points are uniformly distributed.In absence of a rigid dipole moment of the solvent molecules the latter formula may be compared with that implicity deduced by Buckingham for the Kerr effect. In the limit of strong dipoles the orientation imposed by the rigid dipole moments appears to be the major contribution to the alignment of the non-polar molecule.     

Flow of a Bose-Einstein condensate in a quasi-one-dimensional channel under the action of a piston

The problem of the flow of a Bose—Einstein condensate in a channel under the action of a piston is considered. Problems of this kind are topical in connection with experiments on condensate flow control in quasi-one-dimensional (cigar-shaped) traps, in wh ich the repulsive potential produced by a laser beam focused across the trap acts as a piston. A dispersive shock wave characterized by rapid oscillations of the condensate density and flow velocity is shown to be formed in the condensate flow after some instant of time for an arbitrary law of piston motion. The Whitham averaging method is used to obtain a solution for the main parameters of the dispersive shock wave in the case of a uniformly accelerated piston motion. The evolution of the dispersive shock wave immediately after the breaking time, when the dispersionless solution is well approximated by a cubic parabola for the coordinate dependence of the density, is analyzed in the case of an arbitrary piston motion. Comparison shows good agreement of the numerical calculation with the approximate analytical theory. The developed theory complements the previously considered case of a piston moving with a constant velocity and is important for describing the condensate transport in atomic chips.     

Dynamics of a polymer chain confined in a membrane

We present a Brownian dynamics theory with full hydrodynamics (Stokesian dynamics) for a Gaussian polymer chain embedded in a liquid membrane which is surrounded by bulk solvent and walls. The mobility tensors are derived in Fourier space for the two geometries, namely, a free membrane embedded in a bulk fluid, and a membrane sandwiched by the two walls. Within the preaveraging approximation, a new expression for the diffusion coefficient of the polymer is obtained for the free-membrane geometry. We also carry out a Rouse normal mode analysis to obtain the relaxation time and the dynamical structure factor. For large polymer size, both quantities show Zimm-like behavior in the free-membrane case, whereas they are Rouse-like for the sandwiched membrane geometry. We use the scaling argument to discuss the effect of excluded-volume interactions on the polymer relaxation time.     

Excitation of a wake field by a relativistic electron bunch in a semi-infinite dielectric waveguide

A wake field excited by a relativistic electron bunch in a semi-infinite metal waveguide filled with a dielectric consists of the Vavilov-Cherenkov radiation, the “quenching”-wave field, and transient radiation, which interfere with each other. An exact analytic expression for the transient component of the field of a thin relativistic annular bunch is derived for the first time. The evolution of the space distribution of a field excited by a finite-size electron bunch is numerically calculated. The excitation of the wake field by a periodic train of electron bunches in a finite-length waveguide is studied.     

Vibrational relaxation of a molecule in a dense medium

In this paper we consider some features of vibrational relaxation of a guest molecule in a host matrix. The model system involves a harmonic molecule interacting with a harmonic medium. The molecule-medium coupling was handled by the rotating wave approximation considering linear terms in the intramolecular displacements and high terms in the medium displacements. Three specific models for the molecule-medium coupling were considered, which involve single phonon decay, vibron-phonon decay and multiphonon decay. Within the framework of the random phase approximation the Heisenberg equations of motion for the system could be expressed in terms of a unified scheme which is valid for both single phonon and multiphonon processes. Explicit solutions were derived utilizing the Wigner-Weisskopf approximation. This generalized formalism was applied for the study of the time evolution of the distribution, the cooling and the heating processes of the oscillator by a thermal field and for the coupling between vibrational relaxation and infra-red emission.     

Diffusion of a low-soluble impurity in a solid matrix

An analytical expression for the concentration profile of a low-soluble diffusant in a sample is derived for a high-capacity diffusion source. The model is checked by determining the diffusion coefficient of yttrium in beryllium.     

Free-field calibration of a pressure gradient receiver in a reflecting water tank using a linear frequency-modulated signal

This work continues a study of the method for constructing the frequency dependence for a projector-receiver pair in a free field by complex moving weighted averaging of the frequency dependence for a pair measured in the field of a reflecting water tank. The method is applied to the free-field calibration of a pressure gradient receiver using a reference hydrophone when radiating a complex linear frequency-modulated (LFM) signal. To improve the estimates of this method, we edited the initial frequency dependences using functions in the form of the product of the complex LFM projector current multiplied by the powerlaw function of the LFM signal frequency. We consider ways to use a priori information both to improve the results obtained by complex moving weighted averaging and to estimate the distortions introduced by this method are considered.     

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.     

Radiation of a Cascade near a Plane Interface and in a Planar Layer

In order to detect cosmic rays and ultrahigh-energy neutrinos, a number of experiments based on the detection of radio radiation of cascades initiated by these particles in dense media such as ground ice massifs or lunar regolith have been developed. In most of the experiments, radio radiation is detected at the emission to the atmosphere or cosmic space rather than in a dense medium. Consequently, it is necessary to calculate the radiation of a cascade taking into account an interface between two media. This problem is usually solved numerically by the Monte Carlo method. A simple analytical expression for a radiation field in the wave zone of the less dense medium has been obtained for the case of development of the cascade in the dense medium and the crossing of the interface between two media by radiation. The effect of the third, additional medium on the radiation field of the cascade has also been considered.     

Scattering of a Rayleigh surface acoustic wave by a small-size inhomogeneity in a solid half-space

We use the Born approximation of the perturbation method to solve the problem of scattering of a harmonic Rayleigh surface acoustic wave by a weak-contrast inhomogeneity that is small compared with the wavelength and is located in a solid half-space near its boundary. The material of the inhomogeneity differs from the material of the half-space only in its density. The Rayleigh wave incident on the inhomogeneity is excited by a monochromatic surface force source acting normally to the half-space boundary. We derive expressions for the displacement fields in the scattered spherical compressional and shear (SV- and SH-polarized) waves. Scattering of the Rayleigh wave into a Rayleigh wave is studied in detail. We find expressions for the vertical and horizontal components of the displacement vector in the scattered Rayleigh wave as well as its radiated power. It is shown that the field of the scattered surface wave is mainly formed by vertical oscillations of the inhomogeneity in the field of the incident wave. In this case, the radiated power for the scattered Rayleigh wave formed by vertical motion of the inhomogeneity in the incident-wave field depends on the depth of the inhomogeneity as the fourth power of the function describing the well-known depth dependence of the vertical displacements in the Rayleigh surface wave. Correspondingly, the dependence of the radiated power for the scattered Rayleigh wave formed by horizontal motion of the inhomogeneity depends on its location depth as the fourth power of the depth dependence of the horizontal displacements in the Rayleigh surface wave. We perform calculations of the ratio between the powers of the scattered and incident Rayleigh waves for different ratios between the velocities of the compressional and shear waves in a solid. It is shown that the radiated power for the scattered surface wave decreases sharply with increasing depth of the subsurface-inhomogeneity location. Thus, the scattering of a Rayleigh wave into a Rayleigh wave is fairly efficient only when the location depth of the inhomogeneity does not exceed about one-third of the wavelength of the shear wave in an elastic medium.     

Creation of a monopole in a spinor condensate

We propose a method to create a monopole structure in a multicomponent condensate by applying the basic methods used to create vortices and solitons experimentally in single-component condensates. We also show that by using a two-component structure for a monopole, we can avoid many problems related to the previously suggested three-component monopole. We discuss the observation and dynamics of such a monopole structure, and note that the dynamics of the two-component monopole differs from the dynamics of the three-component monopole.     

Dynamics of a pendulum with a quasiperiodic perturbation

The dynamics of a damped pendulum with a quasiperiodic external perturbation is investigated. It is shown that in contrast to a pendulum with a periodic perturbation, a quasiperiodic perturbation leads to chaos in the weakly nonlinear limit when the peak-to-peak amplitude of the oscillations of the pendulum is small. This effect is attributed to the appearance of saddle states induced by the external perturbation. The analytical conditions for the appearance of chaotic oscillations are obtained by the method of running Lyapunov exponents and by the repeated-averaging technique. Zh. Tekh. Fiz. 67, 1–7 (October 1997)     

Trapping and coherent manipulation of a Rydberg atom on a microfabricated device: a proposal

We propose to apply atom-chip techniques to the trapping of a single atom in a circular Rydberg state. The small size of microfabricated structures will allow for trap geometries with microwave cut-off frequencies high enough to inhibit the spontaneous emission of the Rydberg atom, paving the way to complete control of both external and internal degrees of freedom over very long times. Trapping is achieved using carefully designed electric fields, created by a simple pattern of electrodes. We show that it is possible to excite, and then trap, one and only one Rydberg atom from a cloud of ground state atoms confined on a magnetic atom chip, itself integrated with the Rydberg trap. Distinct internal states of the atom are simultaneously trapped, providing us with a two-level system extremely attractive for atom-surface and atom-atom interaction studies. We describe a method for reducing by three orders of magnitude dephasing due to Stark shifts, induced by the trapping field, of the internal transition frequency. This allows for, in combination with spin-echo techniques, maintenance of an internal coherence over times in the second range. This method operates via a controlled light shift rendering the two internal states’ Stark shifts almost identical. We thoroughly identify and account for sources of imperfection in order to verify at each step the realism of our proposal.     

Shortening of a laser pulse with a self-modulated phase at the focus of a lens

We found that, at the focus of a chromatic lens, a laser pulse with a self-modulated phase can be shortened due to the radial dependence of the group delay imposed by the lens. Normally, this group delay stretches a short pulse into a long pulse by spreading the arrival time of the pulse at the focus. However, for a pulse with a self-modulated phase, it causes the fields with different phases to overlap, thus resulting in destructive interference that shortens the pulse.     

Excitation of a cavity by a microwave pulse transmitted through a nonreflective cavity compressor

Excitation of a cavity by a phase-modulated pulse transmitted through a chain of nonreflective cavities is considered. It is shown that for a linear frequency-modulated rectangular pulse, the use of a two-cavity compressor increases the energy stored in the cavity fourfold for the same efficiency of its excitation.     

Self-sustained oscillations of a shock wave interacting with a boundary layer on a supercritical airfoil

A theory is proposed of the self-sustaining oscillations of a weak shock on an airfoil in steady, transonic flow. The interaction of the shock with the boundary layer on the airfoil produces displacement thickness fluctuations which convect downstream and generate sound by interaction with the trailing edge. A feedback loop is established when this sound impinges on the shock wave, resulting in the production of further fluctuations in the displacement thickness. The details are worked out for an idealized mean boundary layer velocity profile, but strong support for the basic hypotheses of the theory is provided by a comparison with recent experiments involving the generation of acoustic “tone bursts” by a supercritical airfoil section.     

Can a few fanatics influence the opinion of a large segment of a society?

Models that provide insight into how extreme positions regarding any social phenomenon may spread in a society or at the global scale are of great current interest. A realistic model must account for the fact that globalization, internet, and other means of mass communications have given rise to scale-free networks of interactions between people. We propose a novel model which takes into account the nature of the interactions network, and provides some key insights into this phenomenon. These include, (1) the existence of a fundamental difference between a hierarchical network whereby people are influenced by those that are higher in the hierarchy but not by those below them, and a symmetrical network where person-on-person influence works mutually, and (2) that a few “fanatics” can influence a large fraction of the population either temporarily (in the hierarchical networks) or permanently (in symmetrical networks). Even if the “fanatics” disappear, the population may still remain susceptible to the positions originally advocated by them. The model is, however, general and applicable to any phenomenon for which there is a degree of enthusiasm or susceptibility to in the population.     

Conductance of a quantum wire in a longitudinal magnetic field

We examine the ballistic conductance of a quantum wire in a parallel magnetic field in the presence of several impurities and derive analytic expressions for the transmission coefficient and the conductance in such a system. We show that scattering by impurities leads to a number of sharp peaks near the thresholds of the conductance quantization steps. The number of such peaks is determined by the distance between the impurities and the energy of the scattered particle. We also study the conductivity of a quantum wire in the region where the transport mechanism is diffusive. The conductivity is examined for the case in which charge carriers are scattered by randomly distributed point impurities. We study Shubnikov-de Haas oscillations in such a system. The general oscillation pattern consists of broad minima separated by irregularly spaced sharp peaks of the burst type. Zh. éksp. Teor. Fiz. 113, 1376–1396 (April 1998)