Quotient space solutions of 11-dimensional supergravity

All the Freund-Rubin type solutions of the 11-dimensional supergravity with a simply connected quotient spaceG/H as the compact 7-dimensional manifold are found. Their geometries depend only on the imbedding ofHG and the Riemannian structure ofG/H. In particular, SU₃×SU₂×U₁/SU₂×U₁×U₁, Einstein solutions are discussed in detail.     

On Gell-Mann's λ-matrices,d- andf-tensors,octets, and parametrizations ofS U (3)

The algebra ofS U (3) is developed on the basis of the matrices _i ofGell-Mann, and identities involving the tensorsd _{i j k} andf _{i j k} occurring in their multiplication law are derived. Octets and the tensor analysis of the adjoint groupS U (3)/Z(3) ofS U (3) are discussed. Various explicit parametrizations ofS U (3) are presented as generalizations of familiarS U (2) results.     

Quantum deformation of lorentz group

A one parameter quantum deformationS _μ L(2,ℂ) ofSL(2,ℂ) is introduced and investigated. An analog of the Iwasawa decomposition is proved. The compact part of this decomposition coincides withS _μ U(2), whereas the solvable part is identified as a Pontryagin dual ofS _μ U(2). It shows thatS _μ L(2,ℂ) is the result of the dual version of Drinfeld's double group construction applied toS _μ U(2). The same construction applied to any compact quantum groupG _c is discussed in detail. In particular the explicit formulae for the Haar measures on the Pontryagin dualG _d ofG _c and on the double groupG are given. We show that there exists remarkable 1-1 correspondence between representations ofG and bicovariant bimodules (“tensor bundles”) overG _c . The theory of smooth representations ofS _μ L(2,ℂ) is the same as that ofSL(2,ℂ) (Clebsh-Gordon coefficients are however modified). The corresponding “tame” bicovariant bimodules onS _μ U(2) are classified. An application to 4D ₊ differential calculus is presented. The nonsmooth case is also discussed.     

Interaction induced delocalization of two particles: large system size calculations and dependence on interaction strength

The localization length L₂ of two interacting particles in a one-dimensional disordered system is studied for very large system sizes by an efficient and accurate variant of the Green function method. The numerical results (at the band center) can be well described by the functional form L ₂ =L ₁ [0.5+c(U) L ₁ ] where L₁ is the one-particle localization length and the coefficient depends on the strength U of the on-site Hubbard interaction. The Breit-Wigner width or equivalently the (inverse) life time of non-interacting pair states is analytically calculated for small disorder and taking into account the energy dependence of the one-particle localization length. This provides a consistent theoretical explanation of the numerically found U-dependence of c(U). Received 16 September 1998     

Gauge symmetries of electroweak interactions

By considering the symmetries associated with baryon number and lepton number conservation as gauge symmetries, the underlying gauge symmetry of weak electromagnetic interactions is shown to beSU(2) _L ×U(1)×U(1)Baryon×U(1)_Lepton. If right-handed currents exist on a par with the observed left-handed ones, then the full symmetry of electroweak interactions that emerges isSU(2)_L×SU(2)_R×U(1)_Baryon×U(1)_Lepton. These symmetries offer a rich spectrum of massive neutral gauge bosons, one of which is the massive neutral boson of the standardSU(2) _L ×U(1) _Y model.     

Anisotropy Effects in Nucleation for Conservative Dynamics

We analyze metastability and nucleation in the context of a local version of the Kawasaki dynamics for the twodimensional it anisotropic Ising lattice gas at very low temperature. Let LsubsetZ² be a sufficiently large finite box. Particles perform simple exclusion on L, but when they occupy neighboring sites they feel a binding energy U₁<0 in the horizontal direction and U₂<0 in the vertical direction; we assume U₁ges U₂. Along each bond touching the boundary of L from the outside, particles are created with rate rho=e^Db and are annihilated with rate 1, where b is the inverse temperature and D>0 is an activity parameter. Thus, the boundary of L plays the role of an infinite gas reservoir with density rho. We take Din (U₁,U₁+U₂) where the totally empty (full) configuration can be naturally associated to metastability (stability). We investigate how the transition from empty to full takes place under the dynamics. In particular, we identify the size and some characteristics of the shape of the it critical droplet/ and the time of its creation in the limit as btoinfty. We observe very different behavior in the weakly or strongly anisotropic case. In both case we find that Wulff shape is not relevant for the nucleation pattern.     

Spectra,eigenvectors and overlap functions for representation operators ofq-deformed algebras

Operators of representations corresponding to symmetric elements of theq-deformed algebrasU _q (su_1,1),U _q (so_2,1),U _q (so_3,1),U _q (so _n ) and representable by Jacobi matrices are studied. Closures of unbounded symmetric operators of representations of the algebrasU _q (su_1,1) andU _q (so_2,1) are not selfadjoint operators. For representations of the discrete series their deficiency indices are (1,1). Bounded symmetric operators of these representations are trace class operators or have continuous simple spectra. Eigenvectors of some operators of representations are evaluated explicitly. Coefficients of transition to eigenvectors (overlap coefficients) are given in terms ofq-orthogonal polynomials. It is shown how results on eigenvectors and overlap coefficients can be used for obtaining new results in representation theory ofq-deformed algebras.     

On a nonstandard two-parametric quantum algebra and its connections withU p,q (gl(2)) andU p,q(gl(1/1))

A quantum algebraU _{p, q} (,H,X _±) associated with a nonstandardR-matrix with two deformation parameters (p, q) is studied and, in particular, its universal -matrix is derived using Reshetikhin's method. Explicit construction of the (p, q)-dependent nonstandardR-matrix is obtained through a coloured generalized boson realization of the universal -matrix of the standardU _{p, q}(gl(2)) corresponding to a nongeneric case. General finite dimensional coloured representation of the universal -matrix ofU _{p, q}(gl(2)) is also derived. This representation, in nongeneric cases, becomes a source for various (p, q)-dependent nonstandardR-matrices. Superization ofU _{p, q}(,H,X _±) leads to the super-Hopf algebraU _{p, q}(gl(1/1)). A contraction procedure then yields a (p, q)-deformed super-Heisenberg algebraU _{p, q}(sh(1)) and its universal -matrix.     

Solid-state and atomic features in the valence-band Auger spectra of copper,silver, and gold

High-resolution measurements of the L₃VV, M₄₅VV, and N₆₇VV Auger spectra are reported for copper, silver, and gold, respectively. Qualitative trends in the spectra and experimentally determined values of U_eff/2W (U_eff is the effective energy required to excite two holes on the same atom; W is the d-electron bandwidth) are shown to be consistent with recent predictions by Sawatzky and Cini concerning the relative importance of atomiclike and bandlike features in Auger spectra.     

Characterization of microwave plasma generated in inhomogeneous magnetic field

The paper is devoted to the investigation of the electron cyclotron resonance (ECR) discharge in the decreasing magnetic field in the pressure range from 0.02 Pa to 90 Pa and the absorbed microwave power from 50 W to 400 W. For a discharge characterization we used the floating potentialU _fl and the saturated ion current densityi _sat ⁺ . The influence of the substrate holder presence on the plasma microparameters was studied. It was shown that for the substrate holder located near ECR at pressures below 0.3 Pa mainly the magnitude ofU _fl strongly depends on the pressurep, the absorbed microwave powerP _a, and the position of the substrate holder with respect to ECR. The values ofU _fl in the plasma in which the substrate holder is inserted strongly differ from those in the plasma without the substrate holder.U _fl of low pressuresp<0.05 Pa achieves high positive values of about +50 V and this results in sputtering of chamber walls.     

Essential self-adjointness of operators in ordered hilbert space

LetH ₀0 be a self-adjoint operator acting in a spaceL ²(M, ). It is assumed thatH ₀ e=0, wheree is strictly positive, and that exp(–tH ₀) is positivity preserving fort0. LetV be a real function onM such that its positive part is inL ²(M,e ²) and its negative part is relatively small with respect toH ₀. ThenH=H ₀+V is essentially self-adjoint on the intersection of the domains ofH ₀ andV. This result is applied to Schrödinger operators and to quantum field Hamiltonians.     

Many-body effects in core-level spectroscopy of rare-earth compounds

Many-body effects in core-level photoemission and core-level photoabsorption are discussed for rare-earth systems, especially for Ce and La compounds, both in metallic and insulating forms. Emphasis is put on effects of metallic mixed valency and insulating covalency of 4f electrons on these spectra. For the insulating compound CeO₂, detailed analyses of the 3d core photoemission (3d-XPS) and the 2p core photoabsorption (L₃-XAS) are presented by using the impurity Anderson model with a filled valence band. In order to give a consistent interpretation for 3d-XPS and L₃-XAS, it is shown to be essential to take account of the Coulomb interactions U _fd (between a 4f electron and a photoexcited 5d electron in the L₃-XAS) and -U _dc (between the 5d electron and a core hole), in addition to -U _fc (between the 4f electron and the core hole). Discussions are given on the physical information derived from the analysis, on similarities and differences in spectral features between insulating and metallic systems, and also on some related topics.     

Thermodynamic inequalities for molecular fluids

We consider the application of the classical Gibbs inequality for the Helmholtz free energy to a fluid whose potential energy depends on positions and orientations of the constituent molecules. Properties of the given fluid are related to the properties of a corresponding ‘reference’ fluid whose potential is the unweighted orientational average of the given potential. It is shown that Aˇ-A ₀, where A and A ₀ are the free energies respectively of the given and corresponding reference fluids, and that the high temperature limit of A - A ₀ may be either zero or negative infinite, depending on the nature of the potential. As consequences, it is shown that no general inequality exists relating the entropies of these systems, and that the internal energies U and U ₀ are plausibly expected to satisfy Uˇ-U ₀ at sufficiently high temperature. The case for a general inequality relating U and U ₀ is not decided.     

Analytic scattering theory for many-body systems below the smallest three-body threshold

We consider the Schrödinger operatorH=H ₀+V of a many-body system, whereV is a sum of dilation-analytic, short range (not necessarily local) two-body interactions, together with the associated self-adjoint analytic familyH(z), |Argz|<a, of complex-dilated operators. For eachz we construct the local wave operators and the S-matrix below the smallest 3-body threshold, using abstract stationary scattering theory and the Weinberg-van Winter equation. The diagonal element of the inverse S-matrix describing scattering within the channel in the lowest energy range is proved to be the boundary value of a meromorphic functionL (z)(z), –az<0, whereL (z) is the S-matrix forH(z) on the corresponding cut. Generally, the poles ofL (z) are resolvent resonances, but a resolvent resonance may not be a pole ofL (z), if it is embedded as an eigenvalue in the continuum ofH(z ₀) for a suitablez ₀.     

Automorphisms and symmetries of quantum logics

Given an amalgam of groups then every quantum logicQ ₀ = (L ₀,M ₀) (L ₀ is aσ-orthomodular poset,M ₀ is a full set of states on it) satisfying some reasonable conditions can be embedded in a quantum logicQ = (L, M), in which (1) all the automorphisms ofL form a group ∼-G ₁, (2) all the automorphisms ofM form a group ∼-G ₂, and (3) all the symmetries ofQ form a group ∼-G ₀. The quantum logic of all closed subspaces of a Hilbert spaceH and all its measures satisfies the conditions required fromQ ₀; hence, enlarging it, one can obtain “anything.”     

Necessity of intermediate mass scales in grand unified theories with spontaneously brokenCP invariance

It is demonstrated that the spontaneous breakdown ofCP invariance in grand unified theories requires the presence of intermediate mass scales. The simplest realization is provided by weakly broken left-right symmetry in the context ofSU(2)_L×SU(2)_R×U(1) _B?L model embedded in grand unified theories.     

高次谐波辐射发射特性研究

报告由不同脉冲宽度(半高宽,FWHM)和不同载波-包络相位(CEP,Φ)的激光产生的高次谐波辐射能量输出时间特性即发射特性的研究结果. 计算表明,由宽度为几个周期的激光产生的高次谐波辐射的截止能量明显低于由无限长脉冲宽度激光产生的截止能量ω_max=3.17U_p+I_p(其中ω_max为光子角频率,U_p和I_p分别为激光有质动力势和原子的电离能). 例如,由两周期(FWHM),Φ＝15°的激光产生的高次谐波辐射的截止能量为ω_max=2.90U_p+I_p,此时发射特性单脉冲(即分布单脉冲)具有最大的能量带宽0.86U_p. 脉冲中心位置的载波相位和时间宽度分别为0.94rad(弧度)和1.29rad. 而该激光脉冲在Φ＝-75°时能产生截止能量为ω_max=2.70U_p+I_p,最大能量带宽为0.70U_p的双分布脉冲,其中心位置分别为-0.58rad和2.43rad,宽度分别为1.22rad和1.33rad. 随着激光脉冲宽度的增加,分布单脉冲的能量带宽比时间宽度下降得更快. 对于一定宽度的激光脉冲,所产生的分布单脉冲的能量带宽和时间宽度的CEP依赖性显示出180°的周期结构. 利用这个有趣的特点,在实验上可以通过调节CEP来选择分布脉冲的能量参数,也可用来定位和控制阿秒脉冲的时间参数. 理论分析指出,只要选择合适的阿秒X射线能量带宽,CEP不稳定性对于光电子谱和测量结果的影响将大为降低,甚至在最大程度上消除这种影响. 这些研究结果不仅有助于在物理上深入了解高次谐波辐射的动力学过程,而且对于进一步在实验上优化和选择阿秒单脉冲和双脉冲具有重要的参考和指导意义. 关键词： 高次谐波产生 鞍点方法 谐波发射特性 分布脉冲     

A two-parameter deformation of the universal enveloping algebra ofsl(3, C)

Starting from a certain multi-parameter matrix that satisfies the quantum Yang-Baxter equation, a two-parameter deformation of the universal enveloping algebra of the simple Lie algebrasl(3, C) is derived. It is shown that this has same product relations and antipode as the standard one-parameter deformationU _q(sl(3, C)) but has a different coproduct. It is also shown that there exists a Hopf algebra whose product relations are merely the commutation relations ofsl(3, C) itself, but whose coproduct is different from the usual one for the universal enveloping algebra ofsl(3, C).     

The jordanian deformation of Su(2) and clebsch-gordan coefficients

Representation theory for the Jordanian quantum algebraU _h (sl(2)) is developed using a nonlinear relation between its generators and those of sl(2). Closed form expressions are given for the action of the generators ofU _h (sl(2)) on the basis vectors of finite dimensional irreducible representations. In the tensor product of two such representations, a new basis is constructed on which the generators ofU _h (sl(2)) have a simple action. Using this basis, a general formula is obtained for the Clebsch-Gordan coefficients ofU _h (sl(2)). Some remarkable properties of these Clebsch-Gordan coefficients are derived. Presented at the 6th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 19–21 June 1997.