Quantum superarrivals and information transfer through a time-varying boundary

The time-dependent Schrödinger equation is solved numerically for the case of a Gaussian wave packet incident on a time-varying potential barrier. The time evolving reflection and transmission probabilities of the wave packet are computed for several different time-dependent boundary conditions obtained by reducing or increasing the height of the potential barrier. We show that in the case when the barrier height is reduced to zero, a time interval is found during which the reflection probability is larger (superarrivals) compared to the unperturbed case. We further show that the transmission probability exhibits superarrivals when the barrier is raised from zero to a finite value of its height. Superarrivals could be understood by ascribing the features of a real physical field to the Schrödinger wave function which acts as a carrier through which a disturbance, resulting from the boundary condition being perturbed, prpagates from the barrier to the detectors measuring reflected and transmitted probabilities. The speed of propagation of this effect depends upon the rate of reducing or raising the barrier height, thus suggesting an application for secure information transfer using superarrivals.     

Resonance excitation of intense acoustic beams in crystals of different syngonies

The resonance excitation of an intense elastic wave in a crystal, arising under conditions of the nonspecular reflection of an incident pump wave is described for a crystal geometry close to a cut that allows the existence of a bulk eigenwave satisfying the free boundary condition. It is shown that choosing a crystal surface parallel to the plane of symmetry optimizes reflection resonance due to the coincidence of the excited wave’s intensity maximum and the reflected (parasite) wave’s intensity minimum in the same geometry of reflection. Parameters of resonance are given for a number of crystals with monoclinic, orthorhombic, and hexagonal syngonies.     

固-固无限周期声子晶体中SH波全反射隧穿的谐振理论

利用边界条件推导出SH波在一维固-固声子晶体中的转移矩阵, 得出一维固-固无限周期声子晶体中SH波的色散关系. 通过建立一维固-固无限周期声子晶体的谐振腔模型并利 用共振条件得出SH波的全反射隧穿的波长公式. 利用波长公式研究了SH波全反射隧穿的波长变化规律, 其结果与色散法一致. 解释了一维固-固无限周期声子晶体中SH波的全反射隧穿效应产生的原因. 关键词： 声子晶体 SH波 全反射隧穿 谐振理论     

Boundary states at reflective moving boundaries

We derive and evaluate boundary states for Maxwell’s equations, the linear, and the nonlinear Euler gas-dynamics equations to compute wave reflection from moving boundaries. In this study we use a Discontinuous Galerkin Spectral Element method (DGSEM) with Arbitrary Lagrangian–Eulerian (ALE) mapping for the spatial approximation, but the boundary states can be used with other methods, like finite volume schemes. We present four studies using Maxwell’s equations, one for the linear Euler equations, and one more for the nonlinear Euler equations. These are: reflection of light from a plane mirror moving at constant velocity, reflection of light from a moving cylinder, reflection of light from a vibrating mirror, reflection of sound from a plane wall and dipole sound generation by an oscillating cylinder in an inviscid flow. The studies show that the boundary states preserve spectral convergence in the solution and in derived quantities like divergence and vorticity.     

光在单轴晶体内表面上的反射

基于电磁波边界条件，从几何光学的角度，对单轴日 体内表面上光的反射规律进行了分析和讨论，给出了寻常光和非常光波法线和光线反射的公式，同时指出了上述结果与由费马原理导出的结果是一致的。     

Reflection and transmission phenomena of waves propagating between an isotropic medium and an arbitrarily oriented anisotropic medium

We theoretically analyze waves propagating between an isotropic medium and an anisotropic medium. Closely examining the boundary condition reveals that the phenomenon of nonsymmetrical reflection occurs when the wave propagates from an anisotropic to an isotropic medium. Calculating the reflection of thin films requires correcting the phase change in each reflected trip in the Airy formula. Analytical results of measurement of the elliptical surface of a wave-vector distribution in an anisotropic medium indicate that reflection and transmission still occur when the reflected and the refracted angles are larger than 90 degrees .     

X‐ray third‐order nonlinear plane‐wave Bragg‐case dynamical diffraction effects in a perfect crystal

Two‐wave symmetric Bragg‐case dynamical diffraction of a plane X‐ray wave in a crystal with third‐order nonlinear response to the electric field is considered theoretically. For certain diffraction conditions for a non‐absorbing perfect semi‐infinite crystal in the total reflection region an analytical solution is found. For the width and for the center of the total reflection region expressions on the intensity of the incidence wave are established. It is shown that in the nonlinear case the total reflection region exists below a maximal intensity of the incidence wave. With increasing intensity of the incidence wave the total reflection region's center moves to low angles and the width decreases. Using numerical calculations for an absorbing semi‐infinite crystal, the behavior of the reflected wave as a function of the intensity of the incidence wave and of the deviation parameter from the Bragg condition is analyzed. The results of numerical calculations are compared with the obtained analytical solution.     

Spin-wave reflection from an interface of two Fermi liquids

The boundary condition for the magnetization jump at an interface of two Fermi liquids and the spin current through the interface is rederived. With the use of the derived condition the coefficient of reflection of a spin wave from a boundary of two Fermi liquids for normal incidence is found and applied to the case of interface of phase separated liquid mixture of ³He in ⁴He. The effect of the phase separation boundary on the coherently precessing spin pattern is discussed.     

Resonance compression of an acoustic beam in a crystal

The resonance excitation of an intense acoustic beam in a crystal is described for a special geometry of pump-wave reflection from the crystal surface. The resonance appears in the vicinity of the total internal reflection angle under the condition that the wave field in a compressed reflected beam propagating almost parallel to the surface is close to the volume eigenmode satisfying the free boundary condition. Criteria for the existence of such modes are considered in detail. Conversion conditions are analyzed under which a “parasitic” reflected wave of the same branch as the incident wave is absent and entire energy from the incident wave falls within a narrow intense acoustic beam of another branch. It is shown that, when the surface is chosen parallel to the crystal symmetry plane, the conversion criterion is reduced to the sole condition on the elastic moduli of the medium. Analysis is performed by analytic and numerical methods for skew cuts of monoclinic, rhombic, trigonal, and hexagonal crystals, when the boundary is the symmetry plane, while the sagittal plane has no symmetry. A number of crystals are found in which resonance excitation is very close to conversion.     

声波在水-含气沉积物界面的反射

含气泡海洋沉积物的声学特性是海底探测的重要问题。为了研究气泡存在对水-含气沉积物界面声反射系数的影响,本文基于气泡振动修正的Biot波动方程推导了气泡存在修正的Biot弹性模量,并结合水-沉积物界面的“开孔”边界条件推导了声波从水入射到水-含气沉积物界面的反射系数。数值分析表明气泡的振动导致反射系数呈现显著的频率特性。在气泡共振频率附近,由于气泡的共振引发的强散射和强衰减,使得反射系数很大,无论以何种角度入射,声波都很难进入含气泡的沉积物。本文研究结果表明,气泡半径、含量、声波频率以及入射角度都是影响水-含气沉积物界面反射系数的主要因素。      

正交各向异性板液/固界面的声反射与声透射

采用Legendre正交多项式法,对液/固界面声波反射和透射系数进行求解。利用Legendre正交多项式对正交各向异性板中的位移解进行展开,推导出板中的应力和波动控制方程。联立液/固界面的边界条件和波动控制方程,建立线性无关方程组,用以计算液/固界面的反射和透射系数及Legendre多项式的展开系数,计算所得铝板液/固界面的反射和透射系数与传递矩阵法的计算结果吻合良好。以单向纤维增强复合材料板为例,在不同的方位角下,分析了反射和透射系数随斜入射角度、入射波频率的变化关系,以及板中声场的位移分布。所取Legendre正交多项式截止阶数越大,可用来计算的频厚积范围越大。研究拓展了Legendre正交多项式法的适用范围,为材料力学性能的声学测量提供了理论基础。      

平面波与线性粘弹海底的反射和折射

采用基于广义标准线性体Boltzmann叠加原理的固体流变模型来描述粘弹性海底底质结构,分析了沉积层和基岩的纵、横波速度频散和衰减的特点,计算了海水沉积层界面和沉积层基岩界面位移势反射和折射系数和能量反射和折射系数。结果表明,采取本模型的粘弹性海底的速度频散、衰减和已有文献的实验数据符合较好,能准确的描述海底底质的主要性质,反射和折射系数和声波的频率有关。      

位相光栅衍射的矢量解法

采用矢量理论处理了多台阶位相光栅的衍射问题，用半数值的方法把微分方程转化成广义本征方程。在利用纵向边值关系作模式匹配时，引入了模式变换阵，反射系数阵和透射系数阵，从而获得了计算电磁场振幅系数阵的递推公式，最后求出任意偏振状态下各级透波和反射波的衍射效率。     

振荡介质中平面波的反射

在复金慈堡-朗道方程描述的振荡介质中研究了平面波的反射.从理论上给出了产生反射的条件,导出了反射波和入射波这两个区域的分界线与两种介质分界线的夹角.发现两类反射,一类为回折射产生的反射,对于这类反射,理论上给出了反射角;另一类为纯反射,它与折射无关.理论分析与数值模拟结果均表明：只有当入射角大于临界入射角才会发生反射,而且反射角等于临界入射角;对于纯反射,反射角随波频率增大而增大. 关键词： 复金慈堡-朗道方程 平面波 反射     

Absorbing boundary conditions for scalar waves in anisotropic media. Part 1: Time harmonic modeling

With the ultimate goal of devising effective absorbing boundary conditions (ABCs) for general anisotropic media, we investigate the accuracy aspects of local ABCs designed for the scalar anisotropic wave equation in the frequency domain (time harmonic case). The ABC analyzed in this paper is the perfectly matched discrete layers (PMDL). PMDL is a simple variant of perfectly matched layers (PML) and is equivalent to rational approximation-based local ABCs. Specifically, we derive a sufficient condition for PMDL to accurately absorb wave modes with outgoing group velocities and this condition turns out to be a simple bound on the PMDL parameters. The reflection coefficient derived in this paper clearly reveals that the PMDL absorption is based on group velocities, and not phase velocities, and hence a PMDL can be designed to correctly identify and accurately absorb all outgoing wave modes (even those with opposing signs of phase and group velocities). The validity of the sufficient condition is demonstrated through a series of frequency domain simulations. In part 2 of this paper [S. Savadatti, M.N. Guddati, Absorbing boundary conditions for scalar waves in anisotropic media. Part 2: Time-dependent modeling, J. Comput. Phys. (2010), http://dx.doi.org/10.1016/j.jcp.2010.05.017], the accuracy condition presented here is shown to govern both the well-posedness and accuracy aspects of PMDL designed for transient (time-dependent) modeling of scalar waves in anisotropic media.     

Probability of boundary conditions in quantum cosmology

One of the main interest in quantum cosmology is to determine boundary conditions for the wave function of the universe which can predict observational data of our universe. For this purpose, we solve the Wheeler–DeWitt equation for a closed universe with a scalar field numerically and evaluate probabilities for boundary conditions of the wave function of the universe. To impose boundary conditions of the wave function, we use exact solutions of the Wheeler–DeWitt equation with a constant scalar field potential. These exact solutions include wave functions with well known boundary condition proposals, the no-boundary proposal and the tunneling proposal. We specify the exact solutions by introducing two real parameters to discriminate boundary conditions, and obtain the probability for these parameters under the requirement of sufficient e-foldings of the inflation. The probability distribution of boundary conditions prefers the tunneling boundary condition to the no-boundary boundary condition. Furthermore, for large values of a model parameter related to the inflaton mass and the cosmological constant, the probability of boundary conditions selects an unique boundary condition different from the tunneling type.     

General Boundary Conditions for a Majorana Single-Particle in a Box in (1 + 1) Dimensions

We consider the problem of a Majorana single-particle in a box in (1 + 1) dimensions. We show that the most general set of boundary conditions for the equation that models this particle is composed of two families of boundary conditions, each one with a real parameter. Within this set, we only have four confining boundary conditions—but infinite not confining boundary conditions. Our results are also valid when we include a Lorentz scalar potential in this equation. No other Lorentz potential can be added. We also show that the four confining boundary conditions for the Majorana particle are precisely the four boundary conditions that mathematically can arise from the general linear boundary condition used in the MIT bag model. Certainly, the four boundary conditions for the Majorana particle are also subject to the Majorana condition.     

Reflection of a spherical wave from a plane surface

A simple approach to the reflection of a spherical sound wave from a locally reacting plane surface is developed. The theory is based on a generalization of the method of images, and expresses the reflected wave as a series in terms of the reciprocal of distance from the image source. Although no general proof that this form for the reflected wave satisfies the surface boundary condition to all orders is available, it has been shown that the first five terms of this solution does satisfy the boundary condition, and agrees with the existing exact solutions for this type of reflection.     

Enhanced transmission by a grating composed of left-handed materials

We present a detailed theoretical analysis about the influence of surface polaritons on the transmission properties of electromagnetic waves at the periodically corrugated interface between the vacuum and left-handed material by using nonlinear boundary condition approach. The principle behind this approach is to match the wave fields across the grating interface by using a set of linear wave equation with nonlinear boundary conditions. The resonant transmission of the incident electromagnetic radiation in this structure is feasible within a certain frequency band, where there is a range of frequency over which both the electric permittivity and the magnetic permeability are simultaneously negative. The enhanced transmission is attributed to the coupling of the incident electromagnetic wave with the excited surface polaritons on grating interface. Finally, we present the numerical results illustrating the effect of the structural parameters and angle of incidence on the transmission spectra of a TM polarized electromagnetic wave.     

Reflection amplitudes of boundary Toda theories and thermodynamic Bethe ansatz

We study the ultraviolet asymptotics in A_n affine Toda theories with integrable boundary actions. The reflection amplitudes of non-affine Toda theories in the presence of conformal boundary actions have been obtained from the quantum mechanical reflections of the wave functional in the Weyl chamber and used for the quantization conditions and ground-state energies. We compare these results with the thermodynamic Bethe ansatz derived from both the bulk and (conjectured) boundary scattering amplitudes. The two independent approaches match very well and provide the non-perturbative checks of the boundary scattering amplitudes for Neumann and (+) boundary conditions.