The Characteristic Classes of Morita Equivalent Star Products on Symplectic Manifolds

In this paper we give a complete characterization of Morita equivalent star products on symplectic manifolds in terms of their characteristic classes: two star products ⋆ and ⋆' on (M,ω) are Morita equivalent if and only if there exists a symplectomorphism ψ\colon M M such that the relative class t(⋆, ψ^⋆(⋆')) is 2 π i-integral. For star products on cotangent bundles, we show that this integrality condition is related to Dirac's quantization condition for magnetic charges. Received: 19 July 2001 / Accepted: 23 January 2002     

New physics contribution to neutral trilinear gauge boson couplings

We study the one-loop new physics effects to the CP even triple neutral gauge boson vertices γ ^⋆ γ Z, γ ^⋆ Z Z, Z ^⋆ Z γ and Z ^⋆ ZZ in the context of Little Higgs models. We compute the contribution of the additional fermions in Little Higgs models in the framework of direct product groups where [SU(2)×U(1)]² gauge symmetry is embedded in SU(5) global symmetry and also in the framework of the simple group where SU(N)×U(1) gauge symmetry breaks down to SU(2) _L ×U(1). We calculate the contribution of the fermions to these couplings when T parity is invoked. In addition, we re-examine the MSSM contribution at the chosen point of SPS1a′ and compare with the SM and Little Higgs models.     

α-, β-和γ-Si3N4 高压下的电子结构和相变: 第一性原理研究

本文采用第一性原理框架下的赝势平面波方法结合振动类德拜模型研究了α,β和γ-Si₃N₄在高温下的点阵常数,弹性常数和弹性模量.研究发现三种同质异相体的体模量都很高.β-Si₃N₄在低温下表现出脆性,在高温下则表现出延展性.γ-Si₃N₄在低温和高温下都是脆性的共价化合物.β → γ 相变的相界斜率为正值,说明在较高温度时合成γ-Si₃N₄所需的压强也较高.α → γ 相变的相界可以表示成 P=16.29- 1.835-10^-2 T+9.33945-10^-5T²-2.16759-10^-7T³+2.91795-10^-10T⁴.本文还分析了Si₃N₄同质异相体在高压下的态密度和能带.在α-Si₃N₄中主要是Si-s, p和N-s,p的轨道杂化对晶体的稳定性起作用.α和β-Si₃N₄都具有Γ_V-Γ_C类型的间接带隙(分别是4.9~eV和4.4~eV)而γ-Si₃N₄具有直接带隙(3.9~eV). 研究还发现α-Si₃N₄和β-Si₃N₄的价带顶分别沿着Γ-M和Γ-A方向.本文的计算结果和已有的实验数据是一致的.     

Equivariant <Emphasis Type="Italic">K</Emphasis>-Theory,Generalized Symmetric Products,and Twisted Heisenberg Algebra

 For a space X acted on by a finite group Γ, the product space X ⁿ affords a natural action of the wreath product Γ _n =Γ ⁿ ⋊S _n . The direct sum of equivariant K-groups were shown earlier by the author to carry several interesting algebraic structures. In this paper we study the K-groups of Γ _n -equivariant Clifford supermodules on X ⁿ . We show that is a Hopf algebra and it is isomorphic to the Fock space of a twisted Heisenberg algebra. Twisted vertex operators make a natural appearance. The algebraic structures on ℱ⁻ _Γ(X), when Γ is trivial and X is a point, specialize to those on a ring of symmetric functions with the Schur Q-functions as a linear basis. As a by-product, we present a novel construction of K-theory operations using the spin representations of the hyperoctahedral groups. Received: 3 February 2001 / Accepted: 17 August 2002 Published online: 10 January 2003     

Positivity of energy in five-dimensional classical unified field theories

Five-dimensional classical unified field theories as well as in Yang-Mills theory with gauge group U(1), are described in terms of a Lorentzian five-dimensional space V ₅ with metric tensor y _;; which admits a space-like Killing vector ξ^α. It is assumed that: (1) V ₅ has the topology of V ₄×S ¹, S ¹ is a circle and V ₄ is a four-dimensional Lorentzian space that is asymptotically flat and (2) the Einstein tensor Γ_αβ of V ₅ satisfies , where u ^α and v ^β are future oriented time-like vectors with . The spinor approach of Witten, Nester, and Moreschi and Sparling is used to show that the conserved five-dimensional energy momentum vector P ^; is nonspace-like. If P ^;=Γ_αβ=0 then V ₅ must admit a time-like Killing vector. Lichnerowicz's results then imply that V ₅ must be flat. A lower bound for P ⁴ (the mass) similar to that found by Gibbons and Hull is obtained.     

A Riemann–Roch Theorem¶for One-Dimensional Complex Groupoids

We consider a smooth groupoid of the form Σ⋊Γ, where Σ is a Riemann surface and Γ a discrete pseudogroup acting on Σ by local conformal diffeomorphisms. After defining a K-cycle on the crossed product C ₀(Σ)⋊Γ generalising the classical Dolbeault complex, we compute its Chern character in cyclic cohomology, using the index theorem of Connes and Moscovici. This involves in particular a generalisation of the Euler class constructed from the modular automorphism group of the von Neumann algebra L ^∞(Σ)⋊Γ. Received: 1 February 2000 / Accepted: 3 December 2000     

Quantum beats in excitons in Cu2O

A theoretical study is carried out of quantum beats (QB) in the time-dependent intensities of absorption of a test pulse and of spontaneous luminescence in a Cu₂O crystal under conditions of double optical resonance. It is assumed that pumping is effected by a CO₂-laser pulse which dynamically couples the exciton levels 1s(Γ ₅ ⁺ ) and 2p(Γ ₄ ⁻ ,Γ ₅ ⁻ ,Γ ₃ ⁻ Γ ₂ ⁻ ) and splits them into two or three pairs of quasi-energy levels. The frequency of the test pulse is in resonance with the frequency Γ ₅ ⁺ of the exciton. The corresponding intensities for various directions of the electric vector of the pump field E _L, the polarization vector ξ, and the wave vector q of the test pulse are obtained. The frequency of the quantum beats is twice the Rabi frequency, which for different values of E _L, ξ and q contains different sets of matrix elements of the dipole transitions between the levels 1s(Γ ₅ ⁺ ) and 2p(Γ ₄ ⁻ ,Γ ₅ ⁻ ,Γ ₃ ⁻ Γ ₂ ⁻ ). Thus, by measuring the period of the quantum beats it is possible to determine the unknown matrix elements of the indicated transitions. Fiz. Tverd. Tela (St. Petersburg) 39, 844–847 (May 1997)     

Cross section and resonance strength measurements of 19F(p, αγ)16O at Ep= 200–800 keV

An excitation function of the ¹⁹F(p, αγ)¹⁶O reaction has been measured over the proton beam energy range E_p= 200–800 keV using a 4 π NaI summing spectrometer. A new resonance was found at E_R= 237 keV and its properties Γ_R, σ_R and ωγ have been extracted. The strengths of all resonances at E_p= 200–800 keV have been also extracted. The importance of the 1⁺ resonance at E_R= 11 keV is discussed and its width has been estimated taking into account interference effects with the strong 1⁺ resonance at E_R= 340 keV. The reaction rates have been calculated over a wide range of temperatures and compared with the rates of the (p, α₀) and (p, α_π) branches of the ¹⁹F(p, α)¹⁶O reaction. Received: 21 June 1999 / Revised version: 30 September 1999     

Structure of turbulent flows of incompressible fluids and the parametrization of turbulence

The structure of stationary isotropic, homogeneous turbulence in an incompressible fluid with Re ≫ 1 set into motion by a force with amplitude f ₀ and spatial and temporal time scales of r ₀ and τ ₀, respectively, is examined. It is found that, depending on the magnitude of the force that sets the fluid into motion, three fundamentally different turbulent stationary states of the fluid can develop and the dimensionless parameters responsible for transitions from one state to another, γ=f ₀ τ ₀ ² /r ₀ and Γ=γ ^4/3 Re, are determined. It is shown that for γ≪1 and Γ≪1 a Kolmogorov spectrum with E(k)∝1/k ^5/3 develops in the inertial range. During the transition to turbulent flows driven by large amplitude forces f ₀, i.e., during the transition to a regime with γ≪1 and Γ ≫ 1, a segment of the spectrum with E(k)∝1/k ² develops near the viscous range and “detaches” the Kolmogorov spectrum from the viscous range. Further increases in the amplitude f ₀ of the force, i.e., approaching the parameter range with γ≫1 and Γ≫1, causes the entire inertial range to be “occupied” by a spectrum E(k)∝1/k ², and outside the inertial range, large scale structures with a characteristic size extending to γ ^2/5 r ₀ begin to be generated. In the regime with Γ≪1, the power dissipated per unit mass of fluid is independent of the viscosity, but on going to turbulent regimes with Γ≫1, the viscous losses begin to depend on the viscosity of the fluid. The “turn-off” of viscous dissipation for Γ≫1 shows that a drag crisis can occur simply as the source power is increased, without any further conditions. With this method for the excitation of turbulence, the Loitsyanskii integral diverges for arbitrary values of γ and Γ. A physical mechanism is proposed to explain the readjustment of the spectrum of the turbulent fluctuations at different γ and Γ. These results have all been obtained neglecting intermittency. Zh. éksp. Teor. Fiz. 116, 1630–1647 (November 1999)     

Bound states of the muon-antimuon system: Lifetimes and hyperfine splitting

We examine the properties of an atomic system consisting of a muon and antimuon. Expressions are derived for the probability of decay and the hyperfine splitting of the lower levels with allowance for the leading radiative corrections, which are of relative order α. The results for the lifetimes and the ground-state energy are τ(1³ S ₁)=1.7907(8)×10⁻¹² s, τ(1¹ S ₀)=0.59547(33)×10⁻¹² s, and E _hfs (1s)=4.23284(35)×10⁷ MHz. The relative probabilities for the various decay channels are calculated; in particular, for the 1 ³ S ₁ level it is found that Γ (μμ→eeγ)/Γ(μμ→ee)≈15%. Finally, possible applications are discussed. Zh. éksp. Teor. Fiz. 113, 409–431 (February 1998)     

Near-IR laser inelastic electronic light scattering spectroscopy on transitions between ground and excited states of acceptor centers in GaAs and InP crystals

We report the development of a method for recording the low-temperature (T=6 K) near-IR inelastic light scattering spectra and the observation of electronic scattering on the transitions 1s _3/2(Γ₈) → 2s _3/2(Γ₈) between the ground and excited states of different shallow acceptor centers in a n-type semi-insulating crystal si-GaAs (n=1.0 × 10⁸ cm⁻³) and in a doped p-InP crystal (p=3.6×10¹⁷ cm⁻³). Moreover, a new line, associated with the transition 1s _3/2(Γ ₈) → 2p _3/2(Γ₈) and due to a dielectric local mode, recorded for the first time in the spectra of narrow-gap semiconductors, was found in the residual-frequency band in the p-InP spectrum between TO(Γ) and LO (Γ) phonons. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 5, 334–339 (10 March 1998)     

A first experimental approach to the 15O + α elastic scattering

The ¹⁵O(α,α)¹⁵O elastic scattering is investigated using a ¹⁵O radioactive beam and a He gas cell limited by Mylar windows. The width of a ¹⁹Ne state at an excitation energy of 5.35MeV is measured as Γ_α = 3.2±1.6keV, in agreement with charge symmetry estimate.     

Measurement of the cross section for the reaction <Superscript>20</Superscript>Ne(<Emphasis Type="Italic">n,α</Emphasis>)<Superscript>17</Superscript>O in the neutron-energy between 4 and 7 MeV

The cross section for the reaction ²⁰Ne(n, α)¹⁷O was measured in the neutron-energy range 4–7 MeV. An ionization chamber equipped with a Frisch grid combined with a pulse-shape digitizer was used as a detector. Gaseous neon that served as a target on which the reaction being studied proceeded was added to the gas filling the ionization chamber. The partial cross sections for the α ₀, α ₁, α ₂, and α ₃ channels of the reaction ²⁰Ne(n, α)¹⁷O were obtained for the first time.     

Invasion Percolation and the Incipient Infinite Cluster in 2D

 We establish two links between two-dimensional invasion percolation and Kesten's incipient infinite cluster (IIC). We first prove that the k ^th moment of the number of invaded sites within the box [−n, n]×[−n, n] is of order (n ²π _n ) ^k , for k≥1, where π _n is the probability that the origin in critical percolation is connected to the boundary of a box of radius n. This improves a result of Y. Zhang. We show that the size of the invaded region, when scaled by n ²π _n , is tight. Secondly, we prove that the invasion cluster looks asymptotically like the IIC, when viewed from an invaded site v, in the limit |v|→∞. We also establish this when an invaded site v is chosen at random from a box of radius n, and n→∞. Received: 3 December 2000 / Accepted: 3 December 2002 Published online: 18 February 2003 RID="⋆" ID="⋆" Present address: CWI, PNA 3, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands. E-mail:jarai@cwi.nl Communicated by M. Aizenman     

Phase Separation in Random Cluster Models I: Uniform Upper Bounds on Local Deviation

This is the first in a series of three papers that addresses the behaviour of the droplet that results, in the percolating phase, from conditioning the planar Fortuin-Kasteleyn random cluster model on the presence of an open dual circuit Γ₀ encircling the origin and enclosing an area of at least (or exactly) n ². (By the Fortuin-Kasteleyn representation, the model is a close relative of the droplet formed by conditioning the Potts model on an excess of spins of a given type.) We consider local deviation of the droplet boundary, measured in a radial sense by the maximum local roughness, MLR(Γ₀), this being the maximum distance from a point in the circuit Γ₀ to the boundary ∂ of the circuit’s convex hull; and in a longitudinal sense by what we term maximum facet length, MLF(Γ₀), namely, the length of the longest line segment of which the polygon ∂ is formed. The principal conclusion of the series of papers is the following uniform control on local deviation: that there are constants 0 < c < C < ∞ such that the conditional probability that the normalized quantity n ^−1/3(log n )^−2/3MLR lies in the interval [c, C] tends to 1 in the high n-limit; and that the same statement holds for n ^−2/3 (log n )^−1/3 MLF. In this way, we confirm the anticipated n ^1/3 scaling of maximum local roughness, and provide a sharp logarithmic power-law correction. This local deviation behaviour occurs by means of locally Gaussian effects constrained globally by curvature, and we believe that it arises in many radially defined stochastic interface models, including growth models belonging to the Kardar-Parisi-Zhang universality class.     

Quantum Vertex Representations via Finite Groups¶and the McKay Correspondence

We establish a q-analog of our recent work on vertex representations and the McKay correspondence. For each finite group Γ we construct a Fock space and associated vertex operators in terms of wreath products of $Γ×ℂ^× and the symmetric groups. An important special case is obtained when Γ is a finite subgroup of SU ₂, where our construction yields a group theoretic realization of the representations of the quantum affine and quantum toroidal algebras of ADE type. Received: 17 August 1999 / Accepted: 2 December 1999     

QCD coupling constant below 1 GeV in the poincare-covariant model

The behavior of the running coupling constant α _s (Q ²) phenomenologically parameterized in the region of Q < 1 GeV is considered within the framework of the Poincare-covariant quark model in a variety of regimes. An analysis was carried out for pseudoscalar and vector mesons with the lepton masses and decay constants (obtained by the model calculations) required to match their experimental counterparts. It shows that the constant α _s is likely to behave with α_crit = α _s (Q ² = 0) ∼ 0.667 − 0.821 in the case of a frozen regime and α_crit =0.300 − 0.692 for peaked curves, which follows from the experimental values of the leptonic decay constants and masses.     

Electron tunneling in the GaAs/AlAs(111) structures with a smooth potential at heteroboundaries

The effect of smooth interface potential on the electron tunneling in the GaAs/AlAs(111) structures with thin layers is studied using the pseudopotential method. The transition region between the structure components is represented by a half-period of the hexagonal (GaAs) ₃(AlAs)₃ (111) superlattice. It is shown that the allowance for the smooth potential results in a decrease in the Γ-L-mixing, Fano-resonance narrowing, and disappearance of interface states at the GaAs/AlAs(111) interface as compared to the abrupt-interface model. The shifts of the lowest Γ-and L-resonances observed for the structures with the layer thickness <2 nm amount to ∼0.1 eV, which is in good agreement with the behavior of levels in quantum wells. The transmission coefficient of electrons with the energies 0–0.5 eV above the GaAs conduction-band bottom obtained by multivalley calculation is close to that calculated with allowance for the lowest conduction band states Γ ₁ ⁽¹⁾ and Γ ₁ ⁽²⁾ of superlattice and Γ ₁ and L ₁ of binary crystals. This indicates that a two-valley superlattice model of the smooth GaAs/AlAs(111) interface can be developed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 7–13, July, 2007.     

Values of adsorption and surface concentrations of the components in Na-K-Cs alloys

The values of adsorption Γ _i ^(N) and surface concentration X _i ^ω of all the components in alloys of the Na-K-Cs system were determined. The adsorption of cesium Γ_Cs^(N) was found to be > 0, while that for sodium Γ_Na^(N) was < 0 in all ternary alloys. The adsorption of potassium was found to undergo inversion when passing from Γ_K^(N) > 0 in ternary alloys (the ratios being X _Na: X _Cs > 14.4 and X _Cs < 6.5 at %) to the negative value of adsorption Γ_K^(N) in the alloys with X _Na: X _Cs < 14.4 and any cesium concentrations. Using the Na-K-Cs system, it was demonstrated for the first time that conditions ΣΓ _i ^(N) = 0 and ΣX _i ^ω = 1 and are fulfilled in ternary alloys.