Multiplicativity of Completely Bounded p-Norms Implies a New Additivity Result

We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represented by a completely positive (CP), trace-preserving map, when the infimum of S(γ₁₂) − S(γ₁) is restricted to states of the form . We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L ₁ → L _p for L _p spaces defined by the Schatten p-norm on matrices, and give another proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L ₁ → L _p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.     

The Relation Between Instantons and Nucleon structure

A scheme of combining the theory of many instantons and the effective Lagrangian of QCD is proposed to study the nucleon structure. With this approach, the vacuum structure of nonperturbative QCD is discussed and a reasonable potential of quark confinement is obtained. The calculated results of the constituent quark mass and the decay constant of pion agree with experimental data quite well.     

Competition Between Two Excitation-dissociation Channels for Molecular Ions

建立了三原子分子离子XYZ+(XY2+)解离产生多种离子产物时Eα和Eβ两个解离通道之间竞争的理论模型. 实验测量出碎片产物分支比和对两束解离光光强比的依赖关系后,由理论公式对数据进行拟合获得拟合参数,可以计算出两个激发解离通道α和β的激发截面分支比.     

Asymptotically Well-Behaved Input States Do Not Violate Additivity for Conjugate Pairs of Random Quantum Channels

It is now well-known that, with high probability, the additivity of minimum output entropy does not hold for pairs of the random quantum channel and its complex conjugate. We investigate asymptotic behavior of output states of r-tensor powers of such pairs, as the dimension of inputs grows. We compute the limit output states for any sequence of well-behaved inputs, which consist of a large class of input states having a nice set of parameters. Then, we show that among these input states tensor products of Bell states give asymptotically the least output entropy, giving positive mathematical evidence towards additivity of above pairs of channels.     

双压电材料三维界面端部力电耦合场奇异性

基于切口根部物理场的幂级数渐近展开假设,从三维应力平衡方程和麦克斯韦方程组出发,导出关于双压电材料楔形界面切口端部奇性指数的特征微分方程组,并将切口的力电学边界条件表达为奇性指数和特征角函数的组合,从而将双压电材料楔形界面切口端部奇性指数的计算转化为相应边界条件下常微分方程组特征值的求解,运用插值矩阵法求解界面端部若干阶应力奇性指数和相应特征函数.计算结果与已有结果对比表明本文方法的有效性和具有较高的计算精度.     

Fundamental Relation Between Entropy Production and Heat Current

Journal of Statistical Physics - We investigate the fundamental relation between entropy production rate and the speed of energy exchange between a system and baths in classical Markov processes....     

The Relation Between Gauge and Non-Gauge Abelian Models

This work studies the relationship between gauge-invariant and non gauge-invariant Abelian vector models. Following a technique introduced by Harada and Tsutsui, we show that the Proca and the chiral Schwinger models may both be viewed as gauge-fixed versions of genuinely gauge-invariant models. This leads to the proposal that any consistent Abelian vector model with no gauge symmetry can be understood as a gauge theory that had its gauge fixed, which establishes an equivalence between gauge-invariant and non gauge-invariant models. Finally, we show that a gauge-invariant version of the chiral Schwinger model, after integrating out the fermionic degrees of freedom, can be identified with the two-dimensional Stueckelberg model without the gauge-fixing term.     

On the Relation Between Strong Subadditivity and Entanglement

Strong subadditivity is used to improve the triangular inequality for the entropy of tensorproducts by the amount of entanglement.     

Relation Between Shape Equations for Axisymmetric vesicles

In deriving the shape equation for axisymmetric vesicles from the Helfrich free energy the variation must be taken with respect to the contour. It is pointed out that the widely used Helfiich shape equation and the other one given by Peterson were derived by improper variations, hence both equations need to be examined. The validity of the two equations is discussed based on analysis of their relation revealed by two derived first integrals. A newly found exact solution for the general shape equation is studied and the relation of this exact solution of spherical topology with that of the Helfrich shape equation is discussed.     

核子的电磁质量与夸克间距的关系

给出一个简易的核子内部夸克的分布模型,讨论了质子和中子的电磁质量,并结合现有的实验数据给出了夸克间距的大致尺度。     

On the Relation Between Open and Closed Topological Strings

We discuss the relation between open and closed string correlators using topological string theories as a toy model. We propose that one can reconstruct closed string correlators from the open ones by considering the Hochschild cohomology of the category of D-branes. We compute the Hochschild cohomology of the category of D-branes in topological Landau-Ginzburg models and partially verify the conjecture in this case.Acknowledgement A.K. would like to thank Volodya Baranovsky, Ezra Getzler, Kentaro Hori, Dima Orlov, and Sasha Voronov for help at various stages. A.K. is also grateful to the Department of Mathematics of Northwestern University and the Erwin Schrödinger Institute for hospitality while this work was being completed. L. R. is very grateful to Mikhail Khovanov for numerous discussions of the category of matrix factorizations. This work was supported in part by the DOE grant DE-FG03-92-ER40701 and by the NSF grant DMS-0196131.     

The Relation Between Elastic and Total Scatterings from Fractals

The ratio of the elastic and total scattering intensities η(q) = I:(q)/I_t²(q) is studied for fractals of dimension range widely. The results show that it oscillatorily decays with a quantity qR_o where q is the absolute value of the momentum transfer q and R_o the average distance between the nearest neighbor sites of scatters in fractal objects. The locations of valleys and peaks of η are only dependent on fractal dimensions. However, the dependence is very beak and η is almost a constant varying in the range of only several percent for widely different fractal dimensions.     

On the Relation Between Casimir Forces and Bulk Correlations

Within a microscopic approach we show that in the case of an ideal quantum gas enclosed in a slit the Casimir force can be simply expressed in terms of the bulk one-particle density matrix. The corresponding formula, which holds both for bosons and fermions, allows to relate the range of the Casimir force to the bulk correlation length. The low-temperature behavior of the Casimir forces is derived.     

拉曼放大器中放大的自发拉曼散射与拉曼开-关增益关系的研究

研究了拉曼放大器中放大的自发拉曼散射对拉曼开－关增益的影响，并提出了一种利用自发拉曼散射谱来调整拉曼放大器位曼开－关增益平坦的方法，实验采用4个波长为14xx nm的激光二极管作为抽运源，75km的G．652光纤作为传输介质，获得了C波段附近的光放大，同时对此给出了合理的理论解释。     

Relation Between CPT Violation in Neutrino Masses and Mixings

The neutrino parameters determined from the solar neutrino data and the anti-neutrino parameters determined from KamLAND reactor experiment are in good agreement with each other. However, the best fit points of the two sets differ from each other by about 10⁻⁵ eV² in mass-square difference and by about 2° in the mixing angle. Future solar neutrino and reactor anti-neutrino experiments are likely to reduce the uncertainties in these measurements. This, in turn, can lead to a signal for CPT violation in terms a non-zero difference between neutrino and anti-neutrino parameters. In this paper, we propose a CPT violating mass matrix which can give rise to the above differences in both mass-squared difference and mixing angle and study the constraints imposed by the data on the parameters of the mass matrix.     

On the Relation Between Time Representations and Inner Product Spaces

Stable states (particles), ghosts and unstable states (particles) come with different types of time representations in unitary groups—definite or indefinite. These representations are discussed with respect to the induced inner product spaces as extensions of Hilbert spaces. Unstable particles with their decay channels are treated as higher dimensional probability collectives.     

Relation Between Fluorescence Decays and Temporal Evolution of Excited States

A differential equation system describing the temporal evolution of excited substates and fluorescence emission were tested using a DOPRI algorithm. The numerical solutions show that there is significant difference in the measurable parameters according to the type of connectivity among the excited substates. In the globally connected case, the fluorescence emission exhibits a double exponential behavior, and the first moment of the emitted spectrum decays with stretched exponential characterized by β < 1. In the diffusive case the fluorescence emission cannot be always fitted with double exponential, and the first moment of the emitted spectrum may decay with stretched exponential characterized by β > 1. Details of modeling and the possibilities of drawing conclusions are also presented.     

Relation Between Rigid-Body Motion,Isotropic Cones,and Spinors

No Heading Spinors play a role in classical physics, since the fact that the rotation group is not simply connected has consequences for macroscopic bodies. Here we relate the orientations of a rigid body to two-dimensional complex spinors by combining O. Rodrigues parameterization of rotations with Cartans 2:1 identification of spinors with complex isotropic 3-vectors.