Tomography of Nonclassical States

A review of the symplectic tomography method is presented. Superpositions of different types of photon states are considered within the framework of the tomography approach. Such nonclassical photon states as even and odd coherent states, crystallized Schrödinger cat states, and other superposition states are studied using the construction of symplectic tomograms (tomographic symbols) and the star-product formalism for tomograms.     

Probability Collectives for Unstable Particles

Unstable particles, together with their stable decay products, constitute probability collectives that are defined as Hilbert spaces with dimension higher than one, nondecomposable in a particle basis. Their structure is considered in the framework of Birkhoff-von Neumann's Hilbert subspace lattices. Bases with particle states are related to bases with a diagonal scalar product by a Hilbert-bein involving the characteristic decay parameters (in some analogy to the n-bein structures of metrical manifolds). Probability predictions as expectation values, involving unstable particles, have to take into account all members of the higher dimensional collective. For example, the unitarity structure of the S-matrix for an unstable particle collective can be established by a transformation with its Hilbert-bein.     

Entanglement and Non-Locality in Quantum Protocols with Identical Particles

We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose constituents cannot be distinguished and singly addressed are still debated. We clarify why the only approach that avoids incongruities and paradoxes is the one based on the second quantization formalism, whereby it is the entanglement of the modes that can be populated by the particles that really matters and not the particles themselves. Indeed, by means of a metrological and of a teleportation protocol, we show that inconsistencies arise in formulations that force entanglement and non-locality to be properties of the identical particles rather than of the modes they can occupy. The reason resides in the fact that orthogonal modes can always be addressed while identical particles cannot.     

The probability representation of quantum states and integral relations for Hermite and Laguerre polynomials

Some integral relations for orthogonal polynomials are elucidated. We review the generic scheme of the star-product construction and study in detail the star-product scheme based on the tomographic map. The dual star-product operator symbols are also considered and studied. Some integral kernels related to the star-product are calculated and new integral formulas for special functions are derived.     

Entanglement,Identical Particles and the Uncertainty Principle

A new uncertainty relation (UR) is obtained for a system of N identical pure entangled particles if we use symmetrized observables when deriving the inequality. This new expression can be written in a form where we identify a term which explicitly shows the quantum correlations among the particles that constitute the system. For the particular cases of two and three particles, making use of the Schwarz inequality, we obtain new lower bounds for the UR that are different from the standard one.     

一种内混合气溶胶粒子模型光散射的等效性

以包含灰尘、黑碳和水三种成分的单分散内混合初次气溶胶为例,利用消光、吸收、散射效率因子和不对称因子,探讨了以等效折射率描述具有不同成分的内混合气溶胶粒子系统的适用性。结果表明,在尺度参数为0.1～25时不同半径比下,消光、吸收和散射效率因子的等效性较好,相对误差分别在3%、3%和4%以内;不对称因子的等效性相对稍差,相对误差在13%以内。当半径比a/b小于1/5,即内混合体中所含灰尘和黑碳较少时,等效折射率实部和虚部值基本可以确定,而不必考虑尺度参数的影响。用除散射相函数之外的其他光学量来等效时,较为容易找到等效的气溶胶粒子。     

微粒形体特征概率分布函数的光散射频谱分析法

针对微粒(包括生物微粒)光散射测量中微粒形体对测量结果的影响以及形体分布不能实时测量的问题,本文根据光散射测量原理,从微粒群的统计性出发,对散射脉冲的脉宽、脉峰分布及其与微粒大小和形体分布物理动态特征的相互关系进行了系统的分析,得到了微粒形体、微粒大小分布与其散射谱分布的特征关系,提出了等值概率面积确定法则,并据此建立了一种实时由散射谱一体分析获取微粒形体特征分布的方法,得到了较好的实验验证,由此可有效地修正因微粒形体变化而对测量精度的影响,从而为粒度分析仪以及以光散射原理为测量理论的流式细胞仪技术的提升提供了有力的基础。     

A Limit Result for a System of Particles in Random Environment

We consider an infinite system of particles in one dimension, each particle performs independent Sinai’s random walk in random environment. Considering an instant t, large enough, we prove a result in probability showing that the particles are trapped in the neighborhood of well defined points of the lattice depending on the random environment, t and the starting points of the particles. Supported by GREFI-MEFI and Departimento di Mathematica, Universita di Roma II “Tor Vergata”, Italy.     

炸药颗粒压制成型数值模拟

 分析炸药压药过程中细观的力学行为,能够为改进压药工艺和提高炸药元件质量提供理论依据。建立了模压条件下炸药颗粒压制成型的计算模型。模型中炸药颗粒被认为是直径相同的球形颗粒,并按一定规律排列。利用非线性有限元计算方法,对炸药颗粒压制成型过程进行了数值模拟计算,分析了压制过程中炸药颗粒变形、受力和温度变化情况。结果表明：药粒在压缩中存在运动和变形两个阶段。在药粒运动阶段,应力集中主要出现在颗粒与约束面的接触部分;药粒进入了塑性变形后,药粒内部压力迅速升高且压力趋于一致。压缩过程中药粒温度升高,药床接近密实状态时,药床中心处药粒温度最高。     

Uncertainty relations for entangled states

A generalized uncertainty relation for an entangled pair of particles is obtained if we impose a symmetrization rule for all operators that we should employ when doing any calculation using the entangled wave function of the pair. This new relation reduces to Heisenberg’s uncertainty relation when the particles have no correlation and suggests that we can have new lower bounds for the product of position and momentum dispersions.     

Wavefunctions for Particles with Arbitrary Spin

By solving rigorously the relativistic wave equations derived from Bargmann-Wigner equation for arbitrary spin,the relativistic wavefunctions in momentum representation for particles with arbitrary spin are deduced.     

结合计算层析与光学相干层析测量折射率分布

通过将计算层析技术与光学相干层析技术相结合,测量散射介质非均匀折射率分布。该方法测量散射样品折射率分布时,通过光学相干层析技术测量散射样品折射率分布在多个方向上的投影,采用计算层析技术实现对样品折射率分布的层析重建,克服了传统折射率光学测量方法如单纯的基于光学相干层析原理的焦点追迹法和光程匹配法,不能测量散射介质非均匀折射率分布的缺点。采用该方法在实验中对梯度折射率棒的径向相对折射率分布进行层析重建,取得了较好的实验结果。     

光学相干层析成像系统的蒙特卡罗模拟

将光学相干层析成像系统采样臂的光纤与聚焦系统和被测样品作为一个整体来模拟光学相干层析成像信号的形成机理.通过追迹采样光束中每一光子在聚焦系统和被测样品中的随机传输轨迹,来决定该光子对光学相干层析成像信号是否有贡献及贡献大小.对样品IntralipidTM的模拟结果与实验结果表明：1）高散射系数和弱前向散射是引起光学相干层析成像信号随测量深度增加迅速减弱的主要原因;2）对于确定的聚焦系统,光纤的数值孔径有一最佳取值范围.数值孔径太小,则光学相干层析成像信号很弱;数值孔径超出这一范围继续增大,光学相干层析成像信号变化很小.3）当光纤的光轴偏离聚焦系统的光轴h距离时,光学相干层析成像信号随h的增加而减弱.     

荧光分子断层成像正向问题的并行计算

针对荧光分子断层成像中相应于激发光和发射光的两个正向方程必须串行求解的实际情况,提出了一种可同时对两个扩散方程进行求解的并行算法。其思想是通过引入乘子矩阵对耦合方程进行解耦来实现并行计算,并利用有限元方法进行了二维数值模拟,将算法求解所得结果与基于串行方法,以Ralf B．Schulz等提出的并行算法所得到的数值模拟结果进行了综合比较。实验表明,该算法一方面适合于任何大小的斯托克斯频移条件,具有更广泛的适应性;另一方面提高了荧光分子断层成像正向问题的求解速度和精度,从而有利于整个荧光分子断层成像的快速精确求解。     

3-D Phase Object Reconstruction Using Beam-Deflection Iterative Tomography

３－ＤＰｈａｓｅＯｂｊｅｃｔＲｅｃｏｎｓｔｒｕｃｔｉｏｎＵｓｉｎｇＢｅａｍ－ＤｅｆｌｅｃｔｉｏｎＩｔｅｒａｔｉｖｅＴｏｍｏｇｒａｐｈｙ￥ＧＡＯＹｉｑｉｎｇ（ＮａｎｃｈａｎｇＩｎｓｔｉｔｕｔｅｏｆＡｅｒｏｎａｕｔｉｃａｌＴｅｃｈｎｏｌｏｇｙ，Ｎａｎｃｈ...     

Tomography of Binomial States of the Radiation Field

The symplectic, optical, and photon-number tomographic symbols of binomial states of the radiation field are studied. Explicit relations for all tomograms of the binomial states are obtained. Two measures for nonclassical properties of these states are discussed.     

Computing Particle Surface Areas and Contact Areas from Three‐Dimensional Tomography Data of Particulate Materials

Microtomography is an emerging technique for particle and particulate‐materials characterization. To use this technology effectively, robust and accurate computational algorithms are needed to compute relevant particle properties, including particle surface area and particle‐particle contact area. However, the most accurate algorithms that have been developed for computing the exposed (void/solid) surface area in a microtomography image cannot be used directly for computing surface areas or particle‐particle contact areas for individual particles in a dense packing. This paper presents an algorithm for extracting particle contact areas from a digitized, segmented image of a packed granular material, which in turn can be used to find individual particle surface areas (even if the complete surfaces are not exposed because of contacts in the packing). Results show that small errors in the binary surface‐area computations are magnified in the course of determining particle contact areas; the total error in the computation depends mainly on the size of the contact area in voxel units.     

Spin tomography and star-product kernel for qubits and qutrits

Using the irreducible tensor-operator technique, we establish the relation between different forms of spin tomograms. Quantizer and dequantizer operators are presented in simple explicit forms and are specified for the low-spin states. The kernel of the star-product is evaluated for qubits and qutrits, and its connection with a generic formula is found.     

Diffusion-Limited Aggregation with Polygon Particles

Diffusion-limited aggregation (DLA) assumes that particles perform pure random walk at a finite temperature and aggregate when they come close enough and stick together. Although it is well known that DLA in two dimensions results in a ramified fractal structure, how the particle shape influences the formed morphology is still unclear. In this work, we perform the off-lattice two-dimensional DLA simulations with different particle shapes of triangle, quadrangle, pentagon, hexagon, and octagon, respectively, and compare with the results for circular particles. Our results indicate that different particle shapes only change the local structure, but have no effects on the global structure of the formed fractal cluster. The local compactness decreases as the number of polygon edges increases.