莫比乌斯与反演问题

 去年,英国“自然”杂志“新闻与评介”专栏登载约翰·麦道克司(John Maddox)文章,对我国学者陈难先教授应用数论中莫比乌斯定理证明物理上的反演问题,作了高度评价.现请中科院化冶所赫彤同志译述如下,以飨读者.     

修正的莫比乌斯反演公式在晶体对势计算中的应用

将陈-莫比乌斯公式作了进一步推广。用修正的莫比乌斯反演公式解决了Ewald求和的反问题——由晶体中原子所受的总势求得原子间的对势。对几种典型晶体结构,提出了基于迭代法的算法及相应的存储结构。分析了算法的稳定性及误差,并进行了试算。 关键词：     

组合傅里叶变换与曲波变换的图像复原

针对图像复原的病态反问题进行研究,分析了图像复原的数学模型及其病态性,提出了组合傅里叶变换与曲波变换的图像复原(ForCurIR)算法.算法利用傅里叶变换对色噪声和曲波变换对分片光滑图像的稀疏表示特性,将图像复原问题转换成傅里叶变换域约束去卷积和曲波变换域约束去噪问题,最后通过组合傅里叶变换域和曲波变换域收缩法实现去卷积和抑制噪声.实验结果表明:ForCurIR算法很好地再现了图像的边缘等细节信息,复原出的图像在信噪比和视觉质量两方面部有显著的提高.     

小波在求解黑体辐射反问题中的应用

针对黑体辐射反问题,提出将其离散为线性不适定问题,利用小波变换方法进行数值求解.将小波变换和正则化方法相结合,利用小波函数的紧支撑性,将原不适定问题转化为粗子空间上的适定问题.数值模拟结果表明方法可行,重构区域温度分布有效.     

图像变换在物理问题中的应用

结合实例, 对图像变换进行了分类及解析. 讨论了其在物理解题中的应用     

小波变换及其应用

傅里叶变换是信号分析的最基本工具和方法之一,但其本身仍然存在较大的缺陷,例如不能提供信号在时域上的特征.短时傅里叶变换虽然可以在一定程度上弥补该缺陷,但是它的频率分辨率和时间分辨率都十分有限,只是一种折衷的解决办法.小波变换是一种快速发展和比较流行的信号分析方法,它精确地揭示了信号在时间和频率方面的分布特点,可以同时分析信号在时域和频域中的特征,并可用多种分辨率来分析信号,实现信号的有损和无损传送.文章简要地回顾了小波变换的发展历史,介绍了小波变换的基本思想、主要概念、计算方法和计算流程.最后以四个典型的     

Taupin-Takagi方程的变换关系及其物理含意

本文论述了畸变晶体X射线衍射动力学理论中Taupin方程和Takagi方程之间的变换关系,讨论了这一变换的物理意义,指出两者之间的差别可归结为波矢k₀的取向略有差异,而物理实质是一致的。 关键词：     

广义脉冲谱方法的一个新形式及其应用

构造了一种新的、有一定抗噪能力的广义脉冲谱方法(GPST)的计算格式。设计了选取正则参数过程中节省计算量的技巧.最后探讨了方法在地震勘探一维波方程反问题上的应用,进行了数值模拟。     

Cluster variation method and Möbius inversion formula

The cluster variation method is reformulated with the aid of the Möbius inversion formula.     

Quasi-one Dimensional Topological Insulator: Möbius Molecular Devices in Peierls Transition

We show that, assisted by the Peierls transition of lattice, as a quasi-one dimensional (Q1D) tight binding system, a Möbius molecular device can behave as a simple topological insulator. With the Peierls phase transition to form a domain wall, the solitonary zero modes exist as the ground state of this electron-phonon hybrid system, which is protected by the Z₂ topology of the Möbius strip. The robustness of the ground state prevents these degenerate zero modes from their energy spectrum splitting caused by any perturbation.     

Collapse arrest in the space-fractional Schrödinger equation with an optical lattice

The soliton solution and collapse arrest are investigated in the one-dimensional space-fractional Schr?dinger equation with Kerr nonlinearity and optical lattice. The approximate analytical soliton solutions are obtained based on the variational approach, which provides reasonable accuracy. Linear-stability analysis shows that all the solitons are linearly stable. No collapses are found when the Lévy index 1 α≤ 2. For α = 1, the collapse is arrested by the lattice potential when the amplitude of perturbations is small enough. It is numerically proved that the energy criterion of collapse suppression in the two-dimensional traditional Schr?dinger equation still holds in the one-dimensional fractional Schr?dinger equation. The physical mechanism for collapse prohibition is also given.     

Optimized nonadiabatic holonomic quantum computation based on Förster resonance in Rydberg atoms

In this paper, we propose a scheme for implementing the nonadiabatic holonomic quantum computation (NHQC+) of two Rydberg atoms by using invariant-based reverse engineering (IBRE). The scheme is based on Förster resonance induced by strong dipole–dipole interaction between two Rydberg atoms, which provides a selective coupling mechanism to simply the dynamics of system. Moreover, for improving the fidelity of the scheme, the optimal control method is introduced to enhance the gate robustness against systematic errors. Numerical simulations show the scheme is robust against the random noise in control fields, the deviation of dipole–dipole interaction, the Förster defect, and the spontaneous emission of atoms. Therefore, the scheme may provide some useful perspectives for the realization of quantum computation with Rydberg atoms.     

Riemann-Hilbert approach and N double-pole solutions for a nonlinear Schrödinger-type equation

We investigate the inverse scattering transform for the Schrödinger-type equation under zero boundary conditions with the Riemann-Hilbert (RH) approach. In the direct scattering process, the properties are given, such as Jost solutions, asymptotic behaviors, analyticity, the symmetries of the Jost solutions and the corresponding spectral matrix. In the inverse scattering process, the matrix RH problem is constructed for this integrable equation base on analyzing the spectral problem. Then, the reconstruction formula of potential and trace formula are also derived correspondingly. Thus, N double-pole solutions of the nonlinear Schrödinger-type equation are obtained by solving the RH problems corresponding to the reflectionless cases. Furthermore, we present a single double-pole solution by taking some parameters, and it is analyzed in detail.     

Soliton fusion and fission for the high-order coupled nonlinear Schr?dinger system in fiber lasers

With the rapid development of communication technology,optical fiber communication has become a key research area in communications.When there are two signals in the optical fiber,the transmission of them can be abstracted as a high-order coupled nonlinear Schr¨odinger system.In this paper,by using the Hirota’s method,we construct the bilinear forms,and study the analytical solution of three solitons in the case of focusing interactions.In addition,by adjusting different wave numbers for phase control,we further discuss the influence of wave numbers on soliton transmissions.It is verified that wave numbers k₁₁,k₂₁,k₃₁,k₂₂,and k₃₂can control the fusion and fission of solitons.The results are beneficial to the study of all-optical switches and fiber lasers in nonlinear optics.     

phyphox软件介绍及其在物理教学中的应用

全面介绍了基于手机传感器应用的phyphox软件的功能,并对于每种传感器均给出了相应实例来说明并启发其在物理教学中的应用.文章最后尝试总结了phyphox软件的优缺点,并对phyphox在物理教学中的应用前景作了展望和思考,期望对广大物理教师和物理教育研究者提供有益参考.     

薛定谔猫态光场与二能级原子相互作用系统的量子特性

在非旋波近似下,通过采用相干态正交化展开的方法,研究了薛定谔猫态光场与二能级原子相互作用系统中,原子的布局数和光场的反聚束效应,并与旋波近似下的结果进行了对比.在旋波近似与非旋波近似下,讨论了初始光场强度、相干态间的相位角以及失谐量对原子布局数和光场反聚束效应的影响;在非旋波近似下,讨论了强弱耦合情况下光场的反聚束效应.研究结果表明:旋波近似与非旋波近似下,原子的布局数随着初始光场强度的不同,表现出不同的特性;当初始光场强度较小时,旋波近似与非旋波近似下,原子的布局数表现出相同的特性;随着初始光场强度的增大,旋波近似下,原子的布局数将表现出坍塌现象.耦合强度较大时,光场的聚束与反聚束效应在非旋波近似与旋波近似下有较大的区别;非旋波近似下,随着初始光场强度的增大,光场一直处于聚束效应状态;而旋波近似下,光场的聚束效应与反聚束效应交替出现.     

Scattering states of modified Pöschlben Teller potential in D-dimension

We present a new approximation scheme for the centrifugal term, and apply this new approach to the Schrödinger equation with the modified Pöschl-Teller potential in the D-dimension for arbitrary angular momentum states. The approximate analytical solutions of the scattering states are derived. The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the k/2π scale and the calculation formula of the phase shifts are given. The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method (APM).     

Mechanisms and Möbius strips: understanding dynamic processes in annulenes

Exploratory computational studies on annulenes with planar, Möbius, and two‐twist topologies have resulted in new mechanisms to explain facile thermal configuration change (cis‐trans isomerization) for medium‐sized annulenes ([12]‐ to [16]annulene). Möbius π‐bond shifting through both aromatic and antiaromatic transition states, two‐twist π‐bond shifting, and planar nondegenerate π‐bond shifting can all be invoked to explain experimental results. Moreover, a simple bond‐shift rule, which is based on the change in number of trans C?C double bonds (Δtrans), was developed that predicts the topology of the transition state(s) necessary to effect the desired cis‐trans isomerization. The bond‐shift rule was also applied to configuration change in dehydro[12]annulene. Finally, extensive investigation of the [14]annulene hypersurface revealed that numerous Möbius minima exist within 10 kcal/mol of the global minimum. Copyright © 2012 John Wiley & Sons, Ltd.