Semiclassical study on photodetachment of hydrogen negative ion in a harmonic potential confined by a quantum well

We have studied the photodetachment dynamics of the H− ion in a harmonic potential confined in a quantum well for the first time. The closed orbits of the detached electron in a confined harmonic potential are found and the photodetachment spectra of this system are calculated. It is interesting to find that the photodetachment spectra depend sensitively on the size of the quantum well and the harmonic frequency. For smaller size of the quantum well, the harmonic potential can be considered as a perturbation, the interference effect between the returning electron wave bounced back by the quantum well and the initial outgoing wave is very strong, which makes the photodetachment spectra exhibits an irregular saw-tooth structure. With the increase of the size of the quantum well, the photodetachment spectra oscillates complicatedly in the higher energy region. For very large size of the quantum well, the photodetachment spectra approach to the case in a free harmonic potential, which is a regular saw-tooth structure. In addition, the harmonic frequency can also affect the photodetachment spectra of this system greatly. Our work provides a new method for the study of spatially confined low-dimensional systems and may guide the future experimental research for the photodetachment dynamics in the ion trap.

Spherical symmetry breaking in electric, magnetic and toroidal multipole moment radiations in spherical toroidal resonant cavities and optimum-efficiency antennas

This Letter reports the breaking of the spherical symmetry in the complete electromagnetic multipole expansion when its sources are distributed on spherical toroidal surfaces, identifying the specic geometrical and physical changes fromthe familiar case of sources on a spherical surface. In fact, for spherical toroids dened by concentric spherical rings and symmetric conical rings, the boundary conditions at the latter are not compatible in general with integer values for the orbital angular momentum label of the multipole moments: the polar angle eigenfunctions become Legendre functions of order λ and associativity m represented as innite series with a denite parity, and their complementary associated radial functions are spherical Bessel functions of the same order λ. Consequently, the corresponding multipole sources for the electric, magnetic and toroidal moments and their connections are identied within the Debye formalism, and theappropriate outgoing wave Green functions are constructed in the new basis of eigenfunctions of the Helmholtz equation. Our familiarity with the exact solutions, for the cases of the complete sphere and of cylindrical toroids, allow us to give a preliminary account of the electromagnetic elds for the spherical toroids via the integration of their sources and the Green function for resonant cavities and optimum effciency antennas.

Numerical Study on Wave Radiation by a Barge with Large Amplitudes and Frequencies

A two-dimensional boundary element method is used to study the hydrodynamics of a single barge with prescribed motions of large amplitudes and high frequencies. The wave radiation problem is solved in the time domain based on the fully nonlinear potential flow theory. For numerical simulations, special treatments like plunging wave cutting and remeshing approaches are presented in detail. The numerical schemes are verified through comparing with analytical results. Both the generated outgoing wave amplitudes and hydrodynamic coefficients can be calculated with sufficient accuracy. Then, we focus on large heave, sway and roll motions to investigate the nonlinear effects on hydrodynamic forces, respectively. In particular, the heave motion with two frequencies is also simulated to study the interactions between results at different frequencies. It is interesting to see the sum and difference frequency components and the envelopes in time histories as a result. For forces caused by forced sway or roll motions, there are only even-order harmonics for vertical forces and only odd-order harmonics for horizontal forces. Finally, a single body with combined sway, heave and roll motion is studied to examine the interactions between motion modes.

RESONANT STATES IN A ONE-DIMENSIONAL QUANTUM SYSTEM

In this work, the concept of resonant states (RSs) in a finite square quantum well is presented. We first derive the analytic secular transcendental equations for even and odd states by applying the outgoing wave boundary conditions into the one-dimensional Schrödinger’s wave equation. The complex solution of these equations is found using the numerical Newton-Raphson method implemented in MATLAB. We can see in particular, that the RSs present a general class of Eigenstates, which includes bound states, anti-bound states, and normal RSs.

3.2. Participation in the global value chains: imposition of dependency or a chance for development

Статья посвящена исследованию альтернативных вариантов участия периферийных стран в глобальных сетях создания стоимости. Вектор зависимого развития ведет к консервации подчиненного положения стран-аутсорсеров, но способствует созданию рабочих мест, дает доступ к техно­логиям, источникам финансирования, рынкам сбыта. Вектор догоняющего развития направлен на трансформацию экономик стран периферии, но сопряжен с обратным эффектом – завоеванием лидерства только в отраслях уходящей волны. В качестве альтернативы предлагается третий путь – вектор опережающего развития. The article is devoted to the study of alternative options for the participation of peripheral countries in global value chains. The vector of dependent development leads to the conservation of the subordinate position of the outsourcing countries, but provides the creation of jobs, gives access to technologies, sources of financing, and sales markets. The vector of catch-up development is aimed at transforming the economies of the peripheral countries but is associated with the opposite effect - gaining leadership only in the sectors of the outgoing wave. The alternative third way proposed in this article is the vector of advanced development.

Photodetachment of the H– ion in a forced harmonic potential

The photodetachment of a H– ion in a forced harmonic potential driven by a general time-dependent oscillating electric field has been investigated in the semi-classical closed orbit theory for the first time. It is found that the driven electric field frequency can affect the photodetachment cross-section of this system greatly. If the frequency of the driving electric field is equal to the harmonic frequency, a resonance phenomenon occurs in the classical motion of the detached electron. The interference effect between the returning electron wave travelling along the closed orbit with the initial outgoing wave gets stronger, causing the photodetachment cross-section to oscillate in a complicated manner. When the frequency of the driving electric field is unequal to the harmonic frequency, the driving electric field can weaken or strengthen the oscillatory structure in the photodetachment cross-section. In addition, the strength and initial phase in the driving electric field can also influence the photodetachment dynamics of the system. Our work provides a new method for controlling the photodetachment of negative ions in a harmonic potential and may guide future experimental research for cavity dynamics or in the ion trap.

Area and entropy quantization of quantum-corrected Schwarzschild black hole surrounded by quintessence

In this paper, the minimal change in the area and the entropy of quantum-corrected Schwarzschild black hole immersed in the quintessence matter is investigated. Utilizing two different approaches, namely, the periodicity of the outgoing wave and the black hole adiabatic property, the area spectrum is derived, which is independent of both the length scale coming from quantum deformation of the Schwarzschild black hole, and the quintessential state parameter, and which is in agreement with the uniform area spacing originally found by Bekenstein.

Outgoing wave conditions in photonic crystals and transmission properties at interfaces

We analyze the propagation of waves in unbounded photonic crystals. Waves are described by a Helmholtz equation with x-dependent coefficients, the scattering problem must be completed with a radiation condition at infinity. We develop an outgoing wave condition with the help of a Bloch wave expansion. Our radiation condition admits a uniqueness result, formulated in terms of the Bloch measure of solutions. We use the new radiation condition to analyze the transmission problem where, at fixed frequency, a wave hits the interface between free space and a photonic crystal. We show that the vertical wave number of the incident wave is a conserved quantity. Together with the frequency condition for the transmitted wave, this condition leads (for appropriate photonic crystals) to the effect of negative refraction at the interface.

Atmospheric radiation boundary conditions for the Helmholtz equation

This work offers some contributions to the numerical study of acoustic waves propagating in the Sun and its atmosphere. The main goal is to provide boundary conditions for outgoing waves in the solar atmosphere where it is assumed that the sound speed is constant and the density decays exponentially with radius. Outgoing waves are governed by a Dirichlet-to-Neumann map which is obtained from the factorization of the Helmholtz equation expressed in spherical coordinates. For the purpose of extending the outgoing wave equation to axisymmetric or 3D cases, different approximations are implemented by using the frequency and/or the angle of incidence as parameters of interest. This results in boundary conditions called atmospheric radiation boundary conditions (ARBC) which are tested in ideal and realistic configurations. These ARBCs deliver accurate results and reduce the computational burden by a factor of two in helioseismology applications.