S-matrix regularities of two-dimensional σ-models of stiefel manifolds

The S-matrices of the two-dimensional nonlinear O(n+m)/O(n) and O(n+m)/O(n) XO(m) σ-models corresponding to Stiefel and Grassmann manifolds, respectively, are compared in leading order in $\text{1}\text{n}$. It is shown, that after averaging over O(m) labels of the incoming and outgoing particles, the S-matrices of both models become identical. This result explains why commonly expected regularities of the Grassmann models, in particular absence of particle production, are found, modulo an O(m) average, also in Stiefel models.     

Entropy in multiparticle production and ultimate multiplicity scaling

The entropy S = − ΣP(n) ln P(n) of multiplicity distributions of charged particles in hadron-hadron collisions is investigated. The observed linear increase of S with maximum possible CMS rapidity Y_m, S = (0.417 ± 0.009) Y_m, may be a special case of a more general scaling S/Y_m = F(y_c/Y_m, found in (pseudo) rapidity windows |y| <y_c. We predict an ultimate multiplicity scaling in the few TeV region.     

Superconformal coset equivalence from level-rank duality

We construct a one-to-one map between the primary fields of the N = 2 superconformal Kazama-Suzuki models G(m, n, k) and G(k, n, m) based on complex Grassmannian cosets, using level-rank duality of Wess-Zumino-Witten models. We then show that conformal weights, superconformal U(I) charges, modular transformation matrices, and fusion rules are preserved under this map, providing strong evidence for the equivalence of these coset models.     

Electrical conductivity, DSC, XRD, and 7Li NMR studies of rotator crystals n-C21H43COOLi x K(1 − x) (0.33 ≤ x ≤ 0.50), n-C m H(2m + 1)COOLi, and n-C m H(2m + 1)COOK (m = 13, 15, 17, 19, and 21)

Differential scanning calorimetry (DSC) thermograms, X-ray diffraction (XRD) analysis, electrical conductivity (σ), and ⁷Li NMR spectroscopy characterization of n-C _m H_(2m?+?1)COOM solids (M = Li, Na, K; m?=?13, 15, 17, 19, 21) and mixed crystals n-C₂₁H₄₃COOLi _x K_(1???x) (0.25?≤?x?≤?0.75) was performed as a function of temperature. DSC thermograms of n-C _m H_(2m?+?1)COOM revealed several solid-solid phase transitions with large entropy changes. Electrical conductivity studies established that n-C _m H_(2m?+?1)COOLi crystals are poor electrical conductors. In contrast, n-C _m H_(2m?+?1)COOK salts were found to have σ values of 10^???7–10^???8 S·cm^???1. Since the crystal structures and phase-transition temperatures of both n-C _m H_(2m?+?1)COOLi and n-C _m H_(2m?+?1)COOK crystals were similar, they were able to form mixed crystals with the structure n-C _x H_(2m?+?1)COOLi _x K_(1???x). DSC thermograms of the mixed crystals showed a small entropy change at the melting point (ΔS _mp?<?13 J K^???1 mol^???1), in addition, large ΔS values at the solid-solid phase transition temperature. The σ values obtained for mixed crystals were roughly one order of magnitude greater than those determined for n-C₂₁H₄₃COOK crystals. ⁷Li NMR spectra of the mixed crystals recorded at various temperatures suggested that the self-diffusion of Li^?+? ions was excited in the highest-temperature solid phase. Based on these results, we have classified these mixed crystals as rotator crystals.     

A new approach to the use of Auger lineshape effect as a routine technique for characterization of chemical bonding

A new routine technique for the characterization of the Auger signal shape is proposed. The procedure consists of measuring the Auger signal symmetry with respect to the base line, when recorded in the E[dn(E)/dE] derivative mode. The LVV transition of the sulphide ion (S^2?) in several combinations (Me_mS_n) illustrates the analytical possibilities of such an approach.     

Canonical Structure and Symmetries of the Schlesinger Equations

The Schlesinger equations S _(n,m) describe monodromy preserving deformations of order m Fuchsian systems with n + 1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m × m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation of the general Schlesinger equations S _(n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates.     

Photoelectron spectra of pyromellitic dianhydride,dithioanhydride and diimide and of trimellitic anhydride

The photoelectron (He(I)) spectra of the tricyclic tetracarbonyl compounds pyromellitic dianhydride, dithioanhydride and diimide and of the tetracyclic hexacarbonyl compound trimellitic anhydride have been investigated. To aid the interpretation of the main features of the spectra, i.e. the ordering and splitting of the ⁿCO ionisations and the behaviour of the ‘benzenic’ and heteroatom π ionisations, MO calculations based on a ZDO pragmatic model and semiempirical SCF-PP calculations have been carried out. The evolution of the ⁿCO and π_X ionisations upon progressive fusion of anhydride moieties with a benzene nucleus is analysed in detail. The proposed orbital sequences for the n orbitals are: a_g(S⁺) $\text{\$}\text{?}$b_1u(AS⁺) $\text{\$}\text{?}$b_2u(S^?) $\text{\$}\text{?}$b_3g(AS^?) for the tetracarbonyls and a′₁(S⁺) $\text{\$}\text{?}$e′(AS⁺) $\text{\$}\text{?}$a′₂ (AS^?) ≈ e′(S^?) for the hexacarbonyl.     

Stark broadening of isolated lines: calculation of the diagonal multiplet factor for complex configurations (n1l1 n n2l2 m n3l3 p)

Owing to the increasing sensitivity of detectors, accurate line profiles are needed for accurate stellar atmospheres modelling and for laboratory and technological plasmas as well. So, Stark broadening parameters of isolated lines of complex atoms and ions within the impact and quasistatic approximation are needed, even if the atomic abundance of the considered element is low. Angular factors of the diagonal line strength entering the quadrupole term appearing in the semi-classical expression of the width of line broadened by electron or ion perturbers, are needed. The aim of this paper is to extend the previous calculations of this diagonal multiplet factor which were obtained for configurations of the type lⁿ and l₁ ⁿl₂ ^m to more complex configurations in LS coupling. To study the Stark broadening of isolated lines in the impact and quasistatic approximation, we use the semi-classical-perturbation treatment, including both dipole and quadrupole contribution in the expansion of the electrostatic interaction between the optical electron and the perturber. We also use the Fano-Racah algebra. Angular factors of the diagonal line strength entering the quadrupole term appearing in the semi-classical expression of the width of line broadened by electron or ion perturbers, are calculated. New diagonal multiplet factor formulae for more complicated configurations such as (n₁l₁ ⁿ(L_nS_n)n₂l₂ ^m(L_mS_m)n₃l₃ ^p(L_pS_p)) are provided. These formulae can enter the computer Stark semi-classical perturbation codes.     

Complex and quaternionic analyticity in chiral and gauge theories,I

A comparative and systematic study is made of 2-dimensional CP(n) σ-models and new 4-dimensional HP(n) σ-models and their respective embedded U(1) and Sp(1) holonomic gauge field structures. The central theme is complex versus quaternionic analyticity. A unified formulation is achieved by way of Cartan's method of moving frames adapted to the hypercomplex geometries of the harmonic symmetric spaces $\text{CP(n) ≈ SU(n + 1)}\text{SU(n) × U(1)}$ and $\text{HP(n) ≈ Sp(n + 1)}\text{Sp(n) × Sp(1)}$ respectively. Elements of complex Kähler manifolds are applied to a detailed analysis of the CP(n) σ-model and its instanton sector. Generalization to any Kählerian σ-model is manifest. On the basis of Cauchy-Riemann analyticity, Kählerian models are shown to have an infinite number of local continuity equations. In a parallel manner, new 4-dimensional conformally invariant HP(n) σ-models are constructed. Focus is on the latter's hidden local gauge invariance in their holonomy group Sp(n) × Sp(1) which allows a natural embedding of the Sp(1) ≈ SU(2) pure Yang-Mills theory. The associated quaternionic structure is discussed in light of both quaternionic quantum mechanics and Kählerian geometry. In this chiral setting, the SU(2) Yang-Mills duality equations are cast into quaternionic Cauchy-Riemann equations over S⁴ ≈ HP(1), the conformal spacetime. In analogy to the CP(n) case, their rational solutions are the most general (8n ? 3) parameter instantons where the associated algebraic nonlinear equations of the type of Atiyah, Drinfeld, Hitchin, and Manin are now expressed in a new conformally invariant form. Geometrically, the SU(2) instantons solve the Frenet-Serret equations for quaternionic holomorphic curves; they are conformal maps from HP(1) into HP(n) with n their second Chern index. Fueter's quaternionic analysis is presented, then applied: Fueter functions are particularly suited for the solutions of 't Hooft, of Jackiw, Nohl and Rebbi, and of Witten and Peng, as well as the self-dual finite action per unit time solution of Bogomol'nyi, Prasad and Sommerfield. Generalizing the latter, a new solution with unit Chern index and finite action per unit spacetime cell is found. It is expressed in terms of the quaternionic fourfold quasi-periodic Weierstrass Zeta function. Finally the essence of our method is revealed in terms of universal connections over Stiefel bundles; generalization to real, complex and quaternionic classifying Grassmanian σ-models with their embedded SO(m), SU(m) and Sp(m) gauge fields is outlined in terms of gauge invariant projector valued chiral fields. Other outstanding problems are briefly discussed.     

Analytic continuation of the Regge pole residue function

We show that the Regge residue functiony(s) is particularly well suited for performing unitarity bootstrap calculations. The reason is that firstlyy(s) has only one, viz. the right hand, cut along which its value can be evaluated from direct channel unitarity using a parameterfree representation for the partial wave amplitudeS(l, s). Secondly its values for negative real argument follow directly from large-energy scattering with the exchange of one Regge pole in the crossed channel. These values can be evaluated from the sameS(l, s) representation by partial wave sums. Then all one needs for a bootstrap system is an analytic connection of these 2 different pieces of information. We show that this can be achieved by logarithmic dispersion relations. This bootstrap system is supposed to compete favorably with the old unitaryN/D calculations. We finally also propose a new parameter free representation ofS(l, s) which applies equally well as that of Cheng. One main result is that Im α(s) has to decrease exponentially for larges.     

Relative diffusion transform and quantum speedup of computations

It is shown that every function computable in time T(n) and space S(n) on a classical one-dimensional cellular automaton can be computed with certainty in time O(T ^1/2 S) and space $n\sqrt T $ on a quantum computer with relative diffusion transforms (RDTs) on parts of intermediate products of classical computation. However, in the general case, RDTs cannot be implemented by the conventional quantum computer even with oracles for intermediate results. Such a function can be computed only in time O(S4 ^S/2 T/T ₁) on the conventional quantum computer with oracles for the intermediate results of classical computations with time T ₁.     

Classification of reflection matrices related to (super-)Yangians and application to open spin chain models

We present a classification of diagonal, antidiagonal and mixed reflection matrices related to Yangian and super-Yangian R matrices associated to the infinite series so(m), sp(n) and osp(m|n). We formulate the analytical Bethe ansatz resolution for the so(m) and sp(n) open spin chains with boundary conditions described by the diagonal solutions.     

Dynamic behaviours of 2∞ attractor and q-phase transitions at bifurcations in logistic map

Dynamic behaviours of the 2^∞ attractor at the accumulation of period doubling in the logistic map are studied by the sum of the local expansion rates S_n(x₁) of nearby orbits. The variance 〈[S_n(x)]²〉 and algebraic exponent ß_n(x₁) = S_n(x₁)/ln(n) exhibits self-similar structures. The critical bifurcations such as intermittency, band merging and crisis-sudden widening of the chaotic attractor are studied in terms of a q-weighted average Λ(q), (− ∞ < q < ∞) of the coarse-grained local expansion rates Λ of nearby orbitals.     

Quark model relation for kaon charge radii

We derive the equation r²_E(K⁰)/r²_E(K⁺) = -(m²_s ? m²_n)/(2m²_s + m²_n) relating the kaon electric charge radii and the strange (m_s) and non-strange (m_n) quark masses in the nonrelativistic quark model, and suggest an inequality which we expect to hold in the presence of relativistic corrections. New data for these charge radii are presently being analysed by two experimental groups.     

n体聚集过程和联合聚集过程的集团尺寸分布

本文研究n体聚集过程和联合聚集过程的集团分布演化。从广义Smoluchovki方程出发,给出聚集核K(i₁,i₂,…,i_n)=A sumfrom i=1 to n i₁+B(A,B均为常数)的显解;利用聚集核K(i₁,i₂,…,i_n)=(Ai₁+B)(Ai₂+B)…(Ai_n+B)和核K(i₁,i₂,…,i_n)=A sumfrom i=1 to n i₁+B的方程之间的联系,得出核K(i₁,i₂,…,i_n)=S_(i1)S_(i2)…S_(in)(S_K=AK+B)的凝前解。而且,根据联合聚集动力学方程,讨论了聚集和型核分别为K₂(i,j)=i+j,K₃(i,j,k)=i+j+k的集团尺寸分布C_m(t)的长时行为,并将结论推广到一般的联合聚集过程。 关键词：     

The extended phase space of the BRS approach

The origin of the classical BRS symmetry is discussed for the case of a first class constrained system consisting of a 2n-dimensional phase spaceS with free action of a Lie gauge groupG of dimensionm. The extended phase spaceS _ext of the Fradkin-Vilkovisky approach is identified with a globally trivial vector bundle overS with fibreL*(G)L(G), whereL(G) is the Lie algebra ofG andL*(G) its dual. It is shown that the structure group of the frame bundle of the supermanifoldS _ext is the orthosymplectic group OSp(m,m; 2n), which is the natural invariance group of the super Poisson bracket structure on the function spaceC (S _ext). The action of the BRS operator is analyzed for the caseS=R ²ⁿ with constraints given by pure momenta. The breaking of the osp(m,m; 2n)-invariance down to sp(2n–2m) occurs via an intermediate osp(m; 2n–m). Starting from a (2n+2m)-dimensional system with orthosymplectic invariance, different choices for the BRS operator correspond to choosing different 2n-dimensional constraint supermanifolds inS _ext, which in general characterize different constrained systems. There is a whole family of physically equivalent BRS operators which can be used to describe a particular constrained system.     

Relativistic comparison theorems for the Klein-Gordon equation with scalar and vector potentials in d-dimensions

Relativistic comparison theorems are established for discrete eigenvalues of Klein-Gordon equation with vector and scalar potentials in d-dimensions. Theorem 1: If V(λ) and S(λ) depend on a parameter λ, ∂S/∂λ?0, S?0, ∂V/∂λ?0, V?0, E>0, then it follows that ∂En/∂λ?0. Theorem 2: If S₂?S₁?0, 0?V₂?V₁, E>0, then the corresponding eigenvalues are ordered as En(2)?En(1). Theorem 3: If 0?V₂?V₁, S₂?|S₁|, En(1)>0, En(2)>0, then En(2)?En(1). Some illustrative examples are given.     

Supercoherent State and Inhomogeneous Differential Realization of OSP(2, 1) Superalgebra

The supercoherent state of OSP(2, 1) superalgebra is constructed and its propertiesare discussed in detail. The matrix elements of the OSP(2, 1) generators inthe supercoherent state space are calculated. New inhomogeneous differentialrealizations of OSP(2, 1) superalgebra are given.     

Effect of the magnetic anisotropy energy distribution of MnSb clusters on spontaneous magnetization reversal of GaMnSb thin films

Temperature m(T) and time m(t) dependences of the magnetic moment of GaMnSb thin films with MnSb clusters have been measured. The m(t) dependences are straightened in semilogarithmic coordinates m(lnt). The temperature dependences of magnetic viscosity S(T) corresponding to the slope of straight lines m(lnt) have been studied. It have been demonstrated that the behavior of dependences S(T) is governed by the lognormal distribution of the magnetic anisotropy energy of MnSb clusters. It have been found that the behavior of dependences m(T) measured after the films were cooled in zero magnetic field and in magnetic field H = 10 kOe is also governed by the lognormal distribution of the magnetic anisotropy energy of MnSb clusters.