Ensemble average of an arbitrary number of pairs of different eigenvalues using Grassmann integration

An identity satisfied by the eigenvalues of a real-symmetric matrix and an integral representation of a determinant using Grassmann variables are used to show that the ensemble average ofS different pairs of eigenvalues of a GOE is given by (–1) ^S 2^{–S –1/2}(S+1/2).     

On Super-RS Algebra and Drinfeld Realization of Quantum Affine Superalgebras

We describe the realization of the super-Reshetikhin–Semenov-Tian-Shansky (RS) algebra in quantum affine superalgebras, thus generalizing the approach of Frenkel and Reshetikhin to the supersymmetric (and twisted) case. The algebraic homomorphism between the super-RS algebra and the Drinfeld current realization of quantum affine superalgebras is established by using the Gauss decomposition technique of Ding and Frenkel. As an application, we obtain Drinfeld realization of quantum affine superalgebra U_q [osp(1|2)⁽¹⁾] and its degeneration – central extended super-Yangian double DY [osp(12)⁽¹⁾].     

Crystal Structure of Level Zero Extremal Weight Modules

We consider the crystal structure of the level zero extremal weight modules V() using the crystal base of the quantum affine algebra constructed in Duke Math. J. 99 (1999), 455–487. This approach yields an explicit form for extremal weight vectors in the U ^– part of each connected component of the crystal, which are given as Schur functions in the imaginary root vectors. We show the map induces a correspondence between the global crystal base of V() and elements .     

Characters of U q (gl(n))-Reflection Equation Algebra

We list characters (one-dimensional representations) of the reflection equation algebra associated with the fundamental vector representation of the Drinfeld–Jimbo quantum group _q (gl(n)).     

Electron Energy Loss Spectra of the Organic Complexes of Europium

In the electron energy loss spectra (EELS) of the organic europium complexes Eu³⁺ (BTFA)₃TPPO and Eu³⁺(BrBTFA)₃TPPO in a gas phase obtained on excitation by monokinetic beams of electrons of different energies in the range 12–50 eV, we have identified the bands associated with the electron transitions S ₀–S ₁, S ₀–S ₂, and S ₀–S ₃. The connection of these transitions with the structural groups of the complexes is established. The addition of the bromine atom to the phenyl ring of diketonate leads to the rise in the relative intensity of the S ₀–S ₂ band. The singlettriplet transitions manifest themselves in the region 2.5–3.2 eV and contribute to the S ₀–S ₂ band of the electron energy loss spectra.     

Toroidal Braid Group Action and an Automorphism of Toroidal Algebra Uq(sln+1,tor) (n ≥ 2)

Utilizing an action of a modification of the double affine Hecke braid group of type gl_n+1, we obtain an automorphism of the toroidal algebra U_q(sl_n+1) (n 2), which maps two central elements C and k₀ · k_n to k₀ · k_n and C^–1, respectively.     

Resonant generation of even-order harmonics in metal vapors

Generation of the second- and fourth-order harmonics of laser radiation is reported in Mg vapor at the forbidden 3s ²¹ S _o–4s ¹ S _o transition. The conversion efficiency for the second-order harmonics has been measured to be 10^–2% and for the fourth one 10^–8%.     

Yang–Mills Algebra

Some unexpected properties of the cubic algebra generated by the covariant derivatives of a generic Yang–Mills connection over the (s+1)-dimensional pseudo Euclidean space are pointed out. This algebra is Koszul of global dimension 3 and Gorenstein but except for s=1 (i.e. in the two-dimensional case) where it is the universal enveloping algebra of the Heisenberg Lie algebra and is a cubic Artin–Schelter regular algebra, it fails to be regular in that it has exponential growth. We give an explicit formula for the Poincaré series of this algebra and for the dimension in degree n of the graded Lie algebra of which is the universal enveloping algebra. In the four-dimensional (i.e. s=3) Euclidean case, a quotient of this algebra is the quadratic algebra generated by the covariant derivatives of a generic (anti) self-dual connection. This latter algebra is Koszul of global dimension 2 but is not Gorenstein and has exponential growth. It is the universal enveloping algebra of the graded Lie algebra which is the semi-direct product of the free Lie algebra with three generators of degree one by a derivation of degree one.     

Spectral-Luminescence Characteristics of Carbazole, Dibenzofuran, and Dinaphthofuran in the Gas Phase in Excitation by Electrons and Photons

The spectra of electron-energy loss, the excitation functions, and the fluorescence spectra in excitation of carbazole, dibenzofuran, and dinaphthofuran by monoenergetic beams of electrons of different energies are determined. The singlet-triplet transitions S ₀–T ₁ and the singlet-singlet transitions up to S ₀–S ₇ are recorded, which covers the region 2–11 eV. In the spectra of electron-energy loss, bands that refer to the n^ast and ^* transitions are identified. The replacement of the heteroatom of nitrogen by the atom of oxygen in the five-membered ring has no substantial effect on the spectra of electron-energy loss.     

Nonlinear refraction and nonlinear absorption of As2S3 aqueous solution

We report for the first time to our knowledge on the preparation of colloidal solution of chalcogenide semiconductor As₂S₃ by laser ablation and the measurements of its nonlinear-optical characteristics using Z-scan method at the wavelength of Nd:YAG laser radiation ( = 1064 nm, = 25 ns). The nonlinear refractive index was measured to be –7.5 × 10^–18 m² W^–1. Nonlinear absorption coefficient of chalcogenide solution was measured to be 1 cm GW^–1.     

String quantization on group manifolds and the holomorphic geometry of DiffS 1/S 1

The recent results by Bowick and Rajeev on the relation of the geometry of DiffS ¹/S ¹ and string quantization in ^d are extended to a string moving on a group manifold. A new derivation of the curvature formula (–26/12m ³+1/6m) _{n, –m} for the canonical holomorphic line bundle over DiffS ¹/S ¹ is given which clarifies the relation of that bundle with the complex line bundles over infinite-dimensional Grassmannians, studied by Pressley and Segal.This work is supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069     

Bethe's Equation Is Incomplete for the XXZ Model at Roots of Unity

We demonstrate for the six vertex and XXZ model parameterized by = –(q+q^-1)/2±1 that when q^2N=1 for integer N2 the Bethe's ansatz equations determine only the eigenvectors which are the highest weights of the infinite dimensional sl₂ loop algebra symmetry group of the model. Therefore in this case the Bethe's ansatz equations are incomplete and further conditions need to be imposed in order to completely specify the wave function. We discuss how the evaluation parameters of the finite dimensional representations of the sl₂ loop algebra can be used to complete this specification.     

The UV absorption spectrum of the phenyl radical isolated in solid argon

Phenyl radicals have been generated by photodecomposition of nitrosobenzene isolated in solid argon at 12 K. In this medium the origin of the first UV absorption band of nitrosobenzene corresponding to theS ₀ S ₂ transition is found at 30260 cm^–1. Excitation with an excess energy of 2200 cm^–1 results in very efficient photodissociation. The fragments NO and phenyl are stable for many hours. Annealing of the sample above 35 K led to partial recombination and recovery of the absorption spectrum of nitrosobenzene. The UV spectrum of the phenyl radical was obtained in the wavenumber range 25000–45000 cm^–1, apparently without contamination by other species. It shows sharp lines at 25220, 33880, and 34820 cm^–1 and two broader maxima at 38360 and 41060 cm^–1. Of these only the line at 34820 cm^–1 had been assigned to the phenyl radical in earlier work. These data are compared to recent molecular orbital calculations.Dedicated to Prof. F. P. Schäfer on the occasion of his 65th birthday.     

Area-preserving diffeomorphisms and higher-spin algebras

We show that there exists a one-parameter family of infinite-dimensional algebras that includes the bosonicd=3 Fradkin-Vasiliev higher-spin algebra and the non-Euclidean version of the algebra of area-preserving diffeomorphisms of the two-sphereS ² as two distinct members. The non-Euclidean version of the area preserving algebra corresponds to the algebra of area-preserving diffeomorphisms of the hyperbolic spaceS ^1,1, and can be rewritten as . As an application of our results, we formulate a newd=2+1 massless higher-spin field theory as the gauge theory of the area-preserving diffeomorphisms ofS ^1,1.     

q-deformed W-algebras and elliptic algebras

The elliptic algebra A _q,p {sl}(N _c) at the critical level c = –N has an extended center containing trace-like operators t(z). Families of Poisson structures, defining q-deformations of the W _N algebra, are constructed. The operators t(z) also close an exchange algebra when (–p ^1/2) ^NM = q ^–c–N for M . It becomes Abelian when in addition p = q ^Nh where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed W _N algebras depending on the parity of h, characterizing the exchange structures at p q ^Nh as new W _q,p(sl(N)) algebras.     

Fine Structures of the Permittivity and Characteristic Losses of Electrons in Fluorite

Experimental-computational spectra of the permittivity and characteristic losses –Im^–1 for energies in the range 5–21 eV at a temperature of 4.2 K and theoretical spectra of and –Im^–1 of a fluorite crystal are resolved into elementary transition bands. The parameters of transition bands (energies of their maxima E _i, band halfwidths H _i and areas S _i, and oscillator forces f _i) are determined. A correlation of the spectral bands of and –Im^–1is established, and their specific features are elucidated.     

Collisional broadening of Ba I line (553.5 nm) by He or Ar

The Doppler-free line shape of the 6s ^{2 1} S ₀ – 6s ¹6p ^{1 1} P ₁ transition at 553.5 nm in natural Ba in the presence of an argon or helium buffer gas has been measured at 744 K for gas pressures from 0.2 to 100 Torr. Using the measured data for pressures above 5 Torr, the broadening rate coefficients for the half width at half maximum (HWHM) are determined to be (4.9±0.5)10^–9 and (5.0±0.5)10^–9 s^–1 cm^–3 for helium and argon respectively.     

Precise calculation of coulomb binding energies of mesomolecules

The best variational energies obtained to date for the ground states of all -mesomolecules are presented. The results are of rather high accuracy and can serve as a theoretical basis for the experimental study of three-body systems. The energies of thee ^– e ⁺ e ^–,H^– and 1¹ S, 2³ S, 2³ P, 2³ P states ofHe are calculated using the same method.     

Fusion Rules for the Continuum Sectors of the Virasoro Algebra with c=1

The Virasoro algebra with c = 1 has a continuum of superselection sectors characterized by the ground state energy h 0. Only the discrete subset of sectors with h = s ², s ₀, arises by restriction of representations of the SU(2) current algebra at level k=1. The remaining continuum of sectors is obtained with the help of (localized) homomorphisms into the current algebra. The fusion product of continuum sectors with discrete sectors is computed. A new method of determining the sector of a state is used.