MathNMR: spin and spatial tensor manipulations in Mathematica

Spin and spatial tensor manipulations are frequently required to describe the theory of NMR experiments. A Mathematica package is presented here, which provides some of the most common functions for these calculations. Examples are the calculation of matrix representations of operators, commutators, projections, rotations, Redfield matrix elements, matrix decomposition into basis operators, change of basis, coherence filtering, and the manipulation of Hamiltonians. The calculations can be performed for any spin system, containing spins 1/2 and quadrupolar spins alike, subject to computational limitations. The package will be available from upon acceptance of the article.     

Parallel computations of dissipative quantum systems: A nonlinear oscillator in a strict quantum regime

A software package for the numerical study of quantum dissipative systems in the field of photonics and quantum optics is developed in a cluster that includes the graphical user interface. Library of C++ classes for numerical simulation of the time evolution of the density matrix, the mean values of different operators (the mean number of photons, the correlation functions of various orders, quadratic mean fluctuations, etc.), the Poincare section, and various quasi-probability distribution functions including the Wigner function in phase space is created. As an application, the results of calculations for a nonlinear oscillator in a strict quantum regime are obtained.     

The study of wavelength-dependent wavefront aberrations based on individual eye model

Theoretical calculations of the wavelength dependence of the ocular wavefront aberrations are performed with individual eye model. Individual eye model, based on the traditional Gullstrand-Le Grand eye model, has been established with measured individual cornea data, eyeball depth and wavefront aberrations. We analyze the wavelength-dependent wavefront aberrations at 12 different visible wavelengths (between 400 and 750 nm) for eight eyes. The change of defocus with wavelength (longitudinal chromatic aberration, LCA) is noticeable, and in good agreement with the results from references. In most cases, the primary spherical aberration changes significantly with wavelength. In comparison with the primary spherical aberration, the other higher-order wavefront aberrations have a smaller change with wavelength. These results have potential applications in those situations where defocus or higher-order wavefront aberrations information in arbitrary wavelength is required.     

存在初级象差下电子和离子光学系统中刘维定理的应用

在电子和离子光学理论(特别是象差理论)中,广泛地应用了矩阵的运算方法。本文讨论了旋转对称电子光学系统与重叠场(环形电场与非均匀磁场的叠加)离子光学系统中存在初级象差下的变换矩阵,证明了这些变换矩阵的行列式数值恒为1.这个普遍结论是刘维定理的具体应用。这对于电子和离子光学象差理论及计算机辅助设计具有一定意义。 关键词：     

A two-regime probe-forming system for modern nuclear nanoprobes

This paper describes the long version of an optimized probe-forming system based on the divided Russian quadruplet of magnetic quadrupole lenses. The calculations include dominant intrinsic and parasitic lens aberrations. The feature of the system is a two-regime operation. This new versatile system is promising for modern nuclear nanoprobes. The system resolutions expected are presented.     

Determination of spectral characteristics of derivatives of chlorines and bacteriochlorins using quantum-chemical methods

The method and results of calculations of molecular, thermodynamic, and spectral parameters for a number of derivatives of chlorine and bacteriochlorin with additional cycles are described. The calculations were performed using the PM3 and ZINDO/S semiempirical method implemented in the HyperChem 6.0 package with consideration given to the conformational flexibility of the molecules under study.     

隐秘型CCD微摄像镜头光学设计

为了满足隐秘型ＣＣＤ摄像光学系统的广角视场、长工作距离、小空间尺寸、隐蔽性能好、成像质量优良等特殊要求。提出一种以同心透镜作为负组,置孔径光阑于镜头前方的新型反远摄结构。对其设计思想、像差特点进行了分析,并给出了ｆ′＝３６ｍｍ,２ω＝８０°,ｌＦ′／ｆ′＝１１的隐秘型ＣＣＤ微摄像镜头的像差和传函计算曲线     

An RGB-Achromatic Aplanatic Metalens

Optical metalenses offer a compact approach for the development of nanoscale optical devices with various imaging functionalities. Realizing high-quality images using metalenses with large numerical aperture (NA) requires eliminating unwanted optical aberrations. Existing strategies have largely focused only on correcting chromatic aberrations, and a metalens capable of simultaneously correcting chromatic and spherical aberrations has not yet been developed. Here, this issue is addresed by realizing an aplanatic phase profile for a red–green–blue (RGB) achromatic metalens, thereby demonstrating an RGB-achromatic aplanatic metalens. This device consists of crystalline silicon nanostructures and it enables RGB-achromatic aplanatic focusing with an NA of 0.635. The focal length of metalens remains unchanged at the three RGB wavelengths, whereas the associated focal spots are significantly smaller than those of an RGB-achromatic metalens with spherical aberrations. An enhanced RGB imaging resolution is demonstrated, offering exciting opportunities to power up various imaging and display applications using flat metalenses.     

A priori calculations of hyperfine interactions in highly ionized atoms: g-factor measurements on aligned pico-second states populated in nuclear reactions

Calculations of hyperfine interaction strength and life-times of states in highly ionized atoms, using the GRASP atomic structure package, are reported. The calculations aim at providing calibration for Recoil-in-Vacuum nuclear excited state g-factor measurements. The method is outlined and results compared with experiment. Inclusion of decay of higher electronic states is discussed.     

Symbolic Package for Quantum Groups, Noncommutative Algebras, and Logics

This paper describes packages for symbolic calculations in quantum groups, noncommutative differential geometry, and multivalued logic. The package for quantum groups and the program for logic are written in Mathematica 3.0 and/or 4.0. As an example, some results in the logic obtained using these packages are presented.     

Reliability of Neutron Yield Cross Sections on 12 C– 127 I Isotopes in Proton-Induced Reactions Evaluated Using GEANT4 Package for Proton Therapy Applications

The work is aimed at studying the reliability of proton-induced neutron yield cross sections on 12C–127I biological tissue isotopes using the GEANT4 Monte Carlo simulation package, which is commonly applied for dosimetry calculations in proton therapy. Because of the lack of experimental results on the neutron yield for most of the isotopes considered, the simulated cross sections are first compared with theoretical data acquired using the TALYS nuclear reaction package, and the partial reaction cross sections calculated in TALYS are in turn analyzed in comparison with available experimental results. The mismatch between theory and experiment allows one to suggest a significant uncertainty in the calculation of the neutron doses associated with the isotopes under consideration.     

偏心光学系统的中心点亮度的计算

本文讨论了偏心光学系统的中心点亮度计算中所必须考虑的离焦、波差展开式、数值计算等几个主要问题。     

部分相干光学成像系统的光学传递函数和像质评价准则

根据光学成像理论，建立了部分相干成像光学系统的光学传递函数。该函数与非相干成像光学系统传递函数相同，因而部分相干成像和非相干成像两者的光学系统波面像差公差标准也是相同的。这一点解释了显微镜光学系统的光学设计惯用法则：镜头像差公差标准的选择，并不因为采用成像照明方式的不同而有所差异。     

Relativistic energies and transition probabilities for some highly excited levels in singly ionized indium

For some excited levels (n?8), the energies, wavelengths, oscillator strengths and transition probabilities calculations in singly ionized indium have been calculated within the framework of multiconfiguration Hartree-Fock approximation with relativistic corrections (Breit-Pauli Hamiltonian). The wavefunctions and some relativistic corrections have been obtained using MCHF-BP atomic package. Comparisons with other calculations and experiments are presented.     

Area spectrum of horizon and black hole entropy

The European Physical Journal C - A Mathematica package for color summed calculations in QCD (SU(N c )) is presented. Color contractions of any color amplitude appearing in QCD may be performed,...     

First principles calculations of structural phase transformation in CaTe at high pressure

First principles calculations of the total energy of CaTe as a function of unit cell volume have been carried out for the NaCl, MnP and CsCl structures on the basis of density functional theory (DFT). All these calculations are performed with the CRYSTAL06 program package. The sequence of high-pressure phases for CaTe transforms from NaCl phase to an intermediate state with a mixture of NaCl and MnP phases and then to the CsCl phase is obtained, which is in good agreement with the previous experimental results. Several structural properties (equilibrium lattice constant, bulk modulus, etc.) of NaCl structure have been calculated, which are also in agreement with the previous experimental results.     

显微物镜干涉图的计算机处理

提出用泰曼干涉仪检测衍射受限的显微物镜，将实验中拍摄的干涉图形数字化后，经计算机处理，用Ｚｅｎｉｋｅ多项式拟合干涉图，可获得各采样点波像差，峰谷误差及均方根误差和各种几何像差。     

Chiral invariant phase space event generator

The CHIPS model and its first implementation within the GEANT4 simulation software package are considered. Hadron production in the process of nucleon-antinucleon annihilation is used as the basic example showing the structure of the model and corresponding software modeling algorithms. Model calculations of multiplicities and spectra of secondary hadrons in the annihilation process are compared with experimental data.     

宽束和细束电磁复合聚焦球面阴极透镜的象差理论

本文研究了对宽束和细束阴极透镜普遍适用的电磁复合聚焦球面阴极透镜的象差理论。在考虑物场和象场弯曲以及阴极面上磁场和横向电场不为零的情况下,导出了任意理想象面上的一级近轴横向象差和包括色象差在内的全部三级横向象差矩阵公式。所得的结果较为完整、普遍。本文详细讨论了宽束和细束阴极透镜的关系,并用轨迹法和变分法严格证明了:当考虑阴极面逸出电子具有一定的初能量和初角度分布,并采用准规范化电位表示的近轴轨迹方程来讨论系统的理想成象时,宽束和细束两类阴极透镜从象差理论以至导出的三级横向象差、象差系数表示式都可以统一起来。本文采用矢量描写轨迹,运用矩阵表示象差,形式简洁,象差系数积分收敛,适合于计算机计算。 关键词：