Tensor structure from scalar Feynman matroids

We show how to interpret the scalar Feynman integrals which appear when reducing tensor integrals as scalar Feynman integrals coming from certain nice matroids.     

Conformal Geodesics on Vacuum Space-times

 A classification of discrete integrable systems on quad–graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three–dimensional consistency. This property yields, among other features, the existence of the discrete zero curvature representation with a spectral parameter. For all integrable systems of the obtained exhaustive list, the so called three–leg forms are found. This establishes Lagrangian and symplectic structures for these systems, and the connection to discrete systems of the Toda type on arbitrary graphs. Generalizations of these ideas to the three–dimensional integrable systems and to the quantum context are also discussed. Received: 14 February 2002 / Accepted: 22 September 2002 Published online: 8 January 2003 Acknowledgements. This research was partly supported by DFG (Deutsche Forschungsgemeinschaft) in the frame of SFB 288 ``Differential Geometry and Quantum Physics'. V.A. was also supported by the RFBR grant 02-01-00144. He thanks TU Berlin for warm hospitality during the visit when part of this work has been fulfilled. Communicated by L. Takhtajan     

Tensor diffusion level set method for infrared targets contours extraction

A tensor diffusion level set method is presented to extract infrared (IR) targets contour under a sky-mountain-water complex background. The proposed model combines tensor diffusion operator and the eigenvalues of tensor-image into a common energy minimization level set framework. By incorporating the information of image tensor diffusion operator into the external energy term, the level set function can move in a specific way. And eigenvalues of tensor-image are used for the regularization of zero level curves in order to diminish the influence of image ‘clutter’ and noise. An additional benefit of the proposed method is robust to initial conditions. Experimental results show very good performance of the tensor diffusion level set method for IR targets contours extraction.     

Variable Step Random Walks and Self-Similar Distributions

We study a scenario under which variable step random walks give anomalous statistics. We begin by analyzing the Martingale Central Limit Theorem to find a sufficient condition for the limit distribution to be non-Gaussian. We study the case when the scaling index∼ζ is∼1₂. For corresponding continuous time processes, it is shown that the probability density function W(x;t) satisfies the Fokker–Planck equation. Possible forms for the diffusion coefficient are given, and related to W(x,t). Finally, we show how a time-series can be used to distinguish between these variable diffusion processes and Lévy dynamics.     

Pion Tensor Generalized Parton Distributions in a Covariant Constituent Quark Model

The pion tensor generalized parton distributions are evaluated within a covariant, analytic constituent quark model. The generalized form factors for the first two Mellin moments and the probability densities of polarized quarks in the impact parameter space are derived and compared with lattice QCD and quark model results.     

Tensor Product of Distributive Sequential Effect Algebras and Product Effect Algebras

A distributive sequential effect algebra (DSEA) is an effect algebra on which a distributive sequential product with natural properties is defined. We define the tensor product of two arbitrary DSEA’s and we give a necessary and sufficient condition for it to exist. As a corollary we obtain the result (see Gudder, S. in Math. Slovaca 54:1–11, 2004, to appear) that the tensor product of a pair of commutative sequential effect algebras exists if and only if they admit a bimorphism. We further obtain a similar result for the tensor product of a pair of product effect algebras.     

Comment on Ricci Collineations for Type B Warped Space-times

We present two counter examples to paper [2] by Carot et al. and show that the results obtained are correct but not general.     

Plane Symmetric Space-times in Bimetric Relativity Theory

It is established that some of the plane symmetric homogeneous models in Rosen's bimetric relativity are singular.     

Quasiprobability and Probability Distributions for Spin-1/2 States

We develop a Radon-like transformation, in which P quasiprobability distribution for spin-1/2 states is written in terms of the tomographic probability distribution w.     

Correlation Functions, Cluster Functions, and Spacing Distributions for Random Matrices

The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm determinants of matrix-valued kernels. The derivations of the various formulas are somewhat involved. In this article we present a direct approach which leads immediately to scalar kernels for the unitary ensembles and matrix kernels for the orthogonal and symplectic ensembles, and the representations of the correlation functions, cluster functions, and spacing distributions in terms of them.     

Gibbs Distributions for Random Partitions Generated by a Fragmentation Process

In this paper we study random partitions of {1,…,n} where every cluster of size j can be in any of w _j possible internal states. The Gibbs (n,k,w) distribution is obtained by sampling uniformly among such partitions with k clusters. We provide conditions on the weight sequence w allowing construction of a partition valued random process where at step k the state has the Gibbs (n,k,w) distribution, so the partition is subject to irreversible fragmentation as time evolves. For a particular one-parameter family of weight sequences w _j , the time-reversed process is the discrete Marcus–Lushnikov coalescent process with affine collision rate K _i,j = a+b(i+j) for some real numbers a and b. Under further restrictions on a and b, the fragmentation process can be realized by conditioning a Galton–Watson tree with suitable offspring distribution to have n nodes, and cutting the edges of this tree by random sampling of edges without replacement, to partition the tree into a collection of subtrees. Suitable offspring distributions include the binomial, negative binomial and Poisson distributions. Research supported in part by N.S.F. Grant DMS-0405779.     

夸克－胶子等离子体对高能碰撞多重产生的可能描述

以ＱＣＤ袋模型和统计流体力学模型为基础，在二维平衡态近似下得到多重数和质心系能量的关系式，和高能　碰撞非单衍过程产生的多重数实验数据吻合得很好；在三维平衡态近似下得到中心在快度较大区域的产生粒子的源Ⅱ的大小和横动量的关系，关系式和三火球模型计算结果符合．     

Limitations of discrete-time quantum walk on a one-dimensional infinite chain

How well can we manipulate the state of a particle via a discrete-time quantum walk? We show that the discrete-time quantum walk on a one-dimensional infinite chain with coin operators that are independent of the position can only realize product operators of the form $e^{i\xi }A?{\mathbb{1}}_p$, which cannot change the position state of the walker. We present a scheme to construct all possible realizations of all the product operators of the form $e^{i\xi }A?{\mathbb{1}}_p$. When the coin operators are dependent on the position, we show that the translation operators on the position can not be realized via a DTQW with coin operators that are either the identity operator $\mathbb{1}$ or the Pauli operator ${\sigma }_x$.     

Tensor coupling effect on relativistic symmetries

The similarity renormalization group is used to transform the Dirac Hamiltonian with tensor coupling into a diagonal form. The upper(lower) diagonal element becomes a Schr¨odinger-like operator with the tensor component separated from the original Hamiltonian.Based on the operator, the tensor effect of the relativistic symmetries is explored with a focus on the single-particle energy contributed by the tensor coupling. The results show that the tensor coupling destroying(improving) the spin(pseudospin) symmetry is mainly attributed to the coupling of the spin-orbit and the tensor term, which plays an opposite role in the single-particle energy for the(pseudo-) spin-aligned and spin-unaligned states and has an important influence on the shell structure and its evolution.     

Tensor gauge field localization on a string-like defect

This work is devoted to the study of tensor gauge fields on a string-like defect in six dimensions. This model is very successful in localizing fields of various spins only by gravitational interaction. Due to problems of field localization in membrane models we are motivated to investigate if a string-like defect localizes the Kalb–Ramond field. In contrast to what happens in Randall–Sundrum and thick brane scenarios we find a localized zero mode without the addition of other fields in the bulk. Considering the local string defect we obtain analytical solutions for the massive modes. Also, we take the equations of motion in a supersymmetric quantum mechanics scenario in order to analyze the massive modes. The influence of the mass as well as the angular quantum number in the solutions is described. An additional analysis on the massive modes is performed by the Kaluza–Klein decomposition, which provides new details about the KK masses.