BPS States of D=4 ␣N=1 Supersymmetry

We find the combinations of momentum and domain-wall charges corresponding to BPS states preserving 1/4, 1/2 or 3/4 of D=4 N=1 supersymmetry, and we show how the supersymmetry algebra implies their stability. These states form the boundary of the convex cone associated with the Jordan algebra of 4× 4 real symmetric matrices, and we explore some implications of the associated geometry. For the Wess–Zumino model we derive the conditions for preservation of 1/4 supersymmetry when one of two parallel domain-walls is rotated and in addition show that this model does not admit any classical configurations with 3/4 supersymmetry. Our analysis also provides information about BPS states of N=1 D=4 anti-de Sitter supersymmetry. Received: 6 April 2000/ Accepted: 10 September 2000     

Jordanian twist quantization of D=4 Lorentz and Poincaré algebras and D=3 contraction limit

We describe in detail the two-parameter nonstandard quantum deformation of the D=4 Lorentz algebra , linked with a Jordanian deformation of . Using the twist quantization technique we obtain the explicit formulae for the deformed co-products and antipodes. Further extending the considered deformation to the D=4 Poincaré algebra we obtain a new Hopf-algebraic deformation of four-dimensional relativistic symmetries with a dimensionless deformation parameter. Finally, we interpret as the D=3 de Sitter algebra and calculate the contraction limit (R is the de Sitter radius) providing an explicit Hopf algebra structure for the quantum deformation of the D=3 Poincaré algebra (with mass-like deformation parameters), which is the two-parameter light-cone κ-deformation of the D=3 Poincaré symmetry.     

Towards κ-deformed D=4 relativistic field theory

We describe free relativistic fields on noncommutative -deformed D=4 Minkowski space. Three possible types of -deformed Fourier transforms are discussed, related with three different -deformed mass-shell conditions.     

Exact Finite-Size Study of the 2D OCP at Γ=4 and Γ=6

An exact numerical study is undertaken into the finite-N calculation of the free energy and distribution functions for the two-dimensional one-component plasma. Both disk and sphere geometries are considered, with the coupling set equal to 4 and 6. Extrapolation of our data for the free energy is consistent with the existence of a universal term (/12)logN, where denotes the Euler characteristic of the surface, as predicted theoretically. The exact finite-N density profile is shown to give poor agreement with the contact theorem relating the density at contact and potential drop to the pressure in the thermodynamic limit. This is understood theoretically via a known finite-N version of the contact theorem. Furthermore, the ideas behind the derivation of the latter result are extended to give a sum rule for the second moment of the pair correlation in the finite disk, which in the thermodynamic limit converges to the Stillinger–Lovett result.     

On Twisted N = 2 5D Super Yang–Mills Theory

On a five-dimensional simply connected Sasaki–Einstein manifold, one can construct Yang–Mills theories coupled to matter with at least two supersymmetries. The partition function of these theories localises on the contact instantons, however, the contact instanton equations are not elliptic. It turns out that these equations can be embedded into the Haydys–Witten equations (which are elliptic) in the same way the 4D anti-self-dual instanton equations are embedded in the Vafa–Witten equations. We show that under some favourable circumstances, the latter equations will reduce to the former by proving some vanishing theorems. It was also known that the Haydys–Witten equations on product manifolds \({M_5 = M_4 \times \mathbb{R}}\) arise in the context of twisting the 5D maximally supersymmetric Yang–Mills theory. In this paper, we present the construction of twisted N = 2 Yang–Mills theory on Sasaki–Einstein manifolds, and more generally on K-contact manifolds. The localisation locus of this new theory thus provides a covariant version of the Haydys–Witten equation.     

D=ε_0Ε_0条件的理论推导

本文由矢量赫姆霍兹（Ｈｅｌｍｈｏｌｔｚ）定理出发，从理论上导出有介质存在时电位移矢量Ｄ仅由自由电荷决定而与极化电荷无关的条件，并对现有教材所给出的条件加以补充．     

0.5 eV时H++D2(v=0,j=0) 反应的微分、积分截面

基于ab initio势能面(KBNN PES)[1],用耦合通道超球坐标理论研究了碰撞能等于0.5 eV时H D2(v=0,j=0)的积分,微分截面.对于反应性碰撞,计算的积分截面表明由于深势阱的存在使得这一绝热反应产物的分布表现出一种近似的统计行为.计算的微分截面反映该体系存在着长寿命的中间络合物;对于非反应性碰撞(传能过程),平动—平动传能过程更有效,且其积分截面随着转动量子数的增大而显著减少.通过反应性碰撞和非反应性碰撞积分截面的比较,发现在低能碰撞情况,非反应性碰撞更容易进行.     

Experimental study of cesium 5D 5D→6S (nL=9D,11S,7F)energy pooling collisions

We report experimentally the measured rate coefficients for the energy pooling(EP)collisions process Cs(5D) Cs(5D)→Cs(6S) Cs(nL=9D,11S,7F)in cesium densities of 10~(16)-10~(17)cm~(-3).The 5D state was populated via 8S→7P→5D spontaneous emission following two-step pumping 6S→6P_(3/2)→8S. Since the 5D→6P(3.0—3.6μm)fluorescence could not be detected in this experiment,we carried out a relative measurement for the process 6P 5D→6S 7D.The excited-atom density and spatial distribution were mapped by monitoring the absorption of a counterpropagating single-mode laser beam, tuned to 6P_(3/2)→9S_(1/2)transition,which could be translated parallelly to the pump beam.The excited atom densities have been combined with the measured fluorescence ratios to yield EP rate coefficients. The average values for nL=9D,11S and 7F are 8.0±4.0,7.0±3.5,and 9.3±4.6(in units of 10~(-10) cm~3/s),respectively.Influence of the energy transfer process 11S 6S(?)7F 6S on the rate coefficients k_(11S)and k_(7F)is also discussed.     

BOTTOM BARYONS(B=-1)∧_b~0=udb,≡_b~0=usb,≡_b~-=dsb,Ω_b~-=ssb

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介质中电位移矢量D=ε_0E_0的充要条件的通俗证明

用电磁学方法通俗地证明电位移矢量Ｄ与介质无关的充要条件．     

Interface Fluctuations for the D = 1 Stochastic Ginzburg–Landau Equation with Nonsymmetric Reaction Term

We consider a Ginzburg–Landau equation in the interval [?ε^?1, ε^?1], ε>0, with Neumann boundary conditions, perturbed by an additive white noise of strength $\sqrt {\varepsilon } $ and reaction term being the derivative of a function which has two equal–depth wells at ±1, but is not symmetric. When ε=0, the equation has equilibrium solutions that are increasing, and connect ?1 with +1. We call them instantons, and we study the evolution of the solutions of the perturbed equation in the limit ε→0⁺, when the initial datum is close to an instanton. We prove that, for times that may be of the order of ε^?1, the solution stays close to some instanton whose center, suitably normalized, converges to a Brownian motion plus a drift. This drift is known to be zero in the symmetric case, and, using a perturbative analysis, we show that if the nonsymmetric part of the reaction term is sufficiently small, it determines the sign of the drift.     

Stereodynamics of the O（^3p） with H： （D2） （v = O,j =O） reaction

Quasi-classical trajectory theory is used to study the reaction of O（3p） with H2 （D2） based on the ground 3A″ potential energy surface （PES）. The reaction cross section of the reaction O＋H2→＋OH＋H is in excellent agreement with the previous result. Vector correlations, product rotational alignment parameters （P2（j′. k）） and several polarizeddependent differential cross sections are further calculated for the reaction. The product polarization distribution exhibits different characteristics that can be ascribed to different motion paths on the PES, arising from various collision energies or mass factors.     

Quasi-classical trajectory investigation on the stereodynamics of Li ＋ DF（v=1-6,j=0）→LiF＋D reaction

In this paper, the stereodynamics of Li ＋ DF → Li F ＋ D reaction is investigated by the quasi-classical trajectory（QCT）method on the ^2A＇ potential energy surface（PES） at a relatively low collision energy of 8.76 kcal/mol. The scalar properties of the title reaction such as reaction probability and cross section are studied with vibrational quantum number of v = 1–6. The product angular distributions P（θr） and P（φr） are presented in the same vibrational level range. Moreover, two polarization-dependent generalized differential cross sections（PDDCSs）, i.e., the PDDCS00 and PDDCS22＋are calculated as well. These stereodynamical results demonstrate sensitive behaviors to the vibrational quantum numbers.     

≡BARYONS(S=-2,I=1/2)≡~0=uss,≡~-=dss

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Ω BARYONS(S=-3,I=0)Ω~-=sss

<正>Ω~-I(J~P)=0(3/2~+)Status:****The unambiguous discovery in both production and decay was by BARNES 64.The quantum numbers follow from the assignment of the particle to the baryon decuplet.DEUTSCHMANN 78 and BAUBILLIER 78 rule out J=1/2 and find consistency with J=3/2.AUBERT.BE 06 finds from the decay angular distributions ofΞ_c~0→Ω~-K~+andΩ_(c~0)→Ω~-K~+that J=3/2;this depends on the spins of theΞ_c~0 andΩ_c~0 being J=1/2,their supposed values.We have omitted some results that have been superseded by later experiments.See our earlier editions.     

∧ BARYONS(S=-1,I=0)∧~0=uds

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Letter: Generalized Chaplygin Gas with α = 0 and the ΛC D M Cosmological Model

The generalized Chaplygin gas model is characterized by the equation of state . It is generally stated that the case = 0 is equivalent to a model with cosmological constant and dust ( C D M). In this work we show that, if this is true for the background equations, this is not true for the perturbation equations. Hence, the mass spectrum predicted for both models may differ.     

迥然不同的pV=nRθ与pV=nRT

理想气体的状态方程ｐＶ＝ｎＲθ,是依据三个实验定律进行热力学理论推导的结果。根据它可以用理想气体实现热力学温标。ｐＶ＝ｎＲＴ是依据实验事实得到的理想气体绝对温标的定义式。两者的物理意义是不相同的。     

The effect of surface temperature on H2/D2(v = 0, j = 0)–Ni(100) scattering processes

We carry out both four-dimensional (4D×2D) and six-dimensional (6D) quantum dynamics on a parametrically time- and temperature-dependent effective Hamiltonian for H₂/D₂(v = 0,j = 0)–Ni(100) collision process. Such an effective potential was derived within a theoretical framework of mean-field approximation by considering weakly correlated interaction between molecular degrees of freedom, phonon modes and electron– hole pair (elhp) coupling through a Hartree-product-type wave function, where the initial state distribution of the surface modes and elhp coupling were introduced through Bose– Einstein and Fermi– Dirac probability factor, respectively. The temperature-dependent dissociation and state-to-state transition probabilities for H₂/D₂(v = 0,j = 0)–Ni(100) system are depicted as a function of initial kinetic energ of the incoming diatom. Though such effect appears negligibly small for H₂(v = 0,j = 0)–Ni(100) system, it is prominent in the case of D₂(v = 0,j = 0)–Ni(100) collision. It appears that the change of dissociation and transition probabilities of D₂ with the increase of surface temperature is exclusively dictated by the phonon modes directed along Z-axis, but the effect of elhp coupling particularly for transition probabilities is insignificant.