Torus Chiral <Emphasis Type="Italic">n</Emphasis>-Point Functions for Free Boson and Lattice Vertex Operator Algebras

 We obtain explicit expressions for all genus one chiral n-point functions for free bosonic and lattice vertex operator algebras. We also consider the elliptic properties of these functions. Received: 6 May 2002 / Accepted: 4 October 2002 Published online: 24 January 2003 RID="*" ID="*" Partial support provided by NSF DMS-9709820 and the Committee on Research, University of California, Santa Cruz RID="⋆⋆" ID="⋆⋆" Supported by an Enterprise Ireland Basic Research Grant and the Millenium Fund, National University of Ireland, Galway Communicated by L. Takhtajan     

The Weyl Quantization and the Quantum Group Quantization of the Moduli Space of Flat <Emphasis Type="Italic">SU</Emphasis>(2)-Connections on the Torus are the Same

 We prove that, for the moduli space of flat SU(2)-connections on the 2-dimensional torus, the Weyl quantization and the quantization performed using the quantum group of SL(2,C) are the same. This is done by comparing the matrices of the operators associated through the two quantizations to cosine functions. We also discuss the *-product of the Weyl quantization and show that it satisfies the product-to-sum formula for noncommutative cosines on the noncommutative torus. Received: 27 January 2002 / Accepted: 9 September 2002 Published online: 19 December 2002 RID="*" ID="*" Research supported in part by the NSF, award No. DMS 0070690 Communicated by A. Connes     

<Emphasis Type="Italic">EPJdirect</Emphasis>

Quark mass effects are analyzed at high Q² in the current fragmentation region of DIS. It is found that the linear combination F ₂ -2.75F ^c ₂ scales at large Q² and small x. We obtained a lower bound for the ratio F ^c ₂/F ₂ which lies very close to the data from HERA. Received: 14 January 2002 / Revised version: 9 October 2002 Published online: 9 December 2002 RID="a" ID="a" e-mail: ryutin@th1.ihep.su     

Perturbation foundation of <Emphasis Type="Italic">q</Emphasis>-deformed dynamics

In the q-deformed theory the perturbation approach can be expressed in terms of two pairs of undeformed position and momentum operators. There are two configuration spaces. Correspondingly there are two q-perturbation Hamiltonians; one originates from the perturbation expansion of the potential in one configuration space, the other one originates from the perturbation expansion of the kinetic energy in another configuration space. In order to establish a general foundation of the q-perturbation theory, two perturbation equivalence theorems are proved. The first is Equivalence Theorem I: Perturbation expressions of the q-deformed uncertainty relations calculated by two pairs of undeformed operators are the same, and the two q-deformed uncertainty relations undercut Heisenberg's minimal one in the same style. The general Equivalence Theorem II is: for any potential (regular or singular) the expectation values of two q-perturbation Hamiltonians in the eigenstates of the undeformed Hamiltonian are equivalent to all orders of the perturbation expansion. As an example of singular potentials the perturbation energy spectra of the q-deformed Coulomb potential are studied. Received: 6 September 2002 / Revised version: 21 October 2002 / Published online: 14 April 2003 RID="a" ID="a" e-mail: jzzhang@physik.uni-kl.de, jzzhang@ecust.edu.cn     

Covalent magnetism in the RFe <Emphasis Type="Bold">6</Emphasis>Ge <Emphasis Type="Bold">6</Emphasis> series

The electronic structure of the RFe ₆ Ge ₆ compounds ( R = Sc, Lu, Ti, Zr, Hf and Nb) of HfFe ₆ Ge ₆ -type structure has been studied using the muffin-tin Korringa-Kohn-Rostoker method in a non-relativistic approach. The chemical bonding is analyzed based on the l-decomposed site projected densities of states. Spin-dependent changes in the R nd- Fe 3d covalent bond are shown to be responsible for the experimentally observed rise in the Fe moment and hyperfine field upon increasing the R valency. The limited quantitative agreement between theoretical and experimental values is interpreted as being due to a non-negligible orbital moment and to a significant asphericity in the spin density at the iron site. The theoretical results also forecast a strong increase of the Ge(2e) transferred hyperfine field with the R valency. Received 20 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: Thomas.Mazet@lcsm.uhp-nancy.fr RID="b" ID="b"Associé au CNRS (UMR 7555)     

<Emphasis Type="Italic">B</Emphasis> to light meson transition form factors calculated in perturbative QCD approach

We calculate the , (P is the light pseudoscalar meson, V the light vector meson) form factors in the large-recoil limit in the perturbative QCD approach, including both the vector (axial vector) and tensor operators. In general there are two leading components and for the B meson wave functions. We consider both contributions of them. Sudakov effects ( and threshold resummation) are included to regulate the soft end-point singularity. By choosing the hard scale as the maximum virtualities of the internal particles in the hard b quark decay amplitudes, Sudakov factors can effectively suppress the long-distance soft contribution. The hard contribution can be dominant in these approaches. Received: 27 December 2002 / Published online: 5 May 2003 RID="a" ID="a" e-mail: lucd@mail.ihep.ac.cn RID="b" ID="b" e-mail: yangmz@mail.ihep.ac.cn     

<Emphasis Type="Italic">Z</Emphasis>-scan technique through beam radius measurements

A modification to the well-known z-scan technique for measuring optical non-linearities is introduced. It is based on directly measuring the beam radius in the far field instead of the transmittance of the irradiance through an aperture, as in the original version. It has the advantage of being insensitive to beam pointing instability and is almost insensitive to power fluctuations. Furthermore, the calculations required for the determination of the non-linear parameters are simplified. For demonstrating the advantages of the modified method, beam radius and transmittance measurements were simultaneously taken in the standard non-linear optical material CS₂. Separate fittings of these measurements gave almost the same values for the non-linearities, quite similar to those in the literature. A common fitting has been applied to both sets of measurements, enhancing the accuracy of the method. Received: 8 July 2002 / Revised version: 18 October 2002 / Published online: 8 January 2003 RID="*" ID="*"Corresponding author. Fax: +30-2610/997470, E-mail: gianetas@physics.upatras.gr     

Sub-Doppler fluorescence on the atomic <Emphasis Type="Italic">D</Emphasis><Subscript>2</Subscript> line of a submicron rubidium-vapor layer

An extremely thin cell (ETC) with the thickness of a Rb atomic vapor layer in the range of 100–300 nm was fabricated. It is demonstrated that a simple laser-diode technique with a single resonant light beam is sufficient to observe separately all of the atomic hyperfine transitions of the D ₂ line of Rb (780 nm) and also allows us to measure the relative transition probabilities of the hyperfine transitions. The onset of collisional self-broadening of the hyperfine transitions as the number density of atoms increases was studied. The detrimental role of the atoms with slow longitudinal velocity in the sub-Doppler response of the Rb ETC is demonstrated by studies in which the cell is tilted from normal incidence of the laser beam. It is also shown that using an ETC allows us to resolve in a moderate external magnetic field the Zeeman splitting of the hyperfine transitions of the ⁸⁷Rb D ₁ transition F _g=1F _e=1,2. Received: 19 February 2003 / Revised version: 4 April 2003 / Published online: 2 June 2003 RID="*" ID="*"Corresponding author. Fax: +374/32-31172, E-mail: david@ipr.sci.am     

Infrared absorption-edges of molecular nonlinear optical crystals: an <Emphasis Type="Italic">ab initio</Emphasis> calculation

A theoretical model suitable for calculating infrared absorption-edges of molecular nonlinear optical (NLO) crystals is introduced from high-level calculations of molecular vibrational spectra. The model is useful for elucidating the relationship between the molecular vibration and macroscopic absorption edges on the IR side of organic nonlinear optical crystals. The first-principle ab initio method carries out the calculations of IR absorption-edges of several typical molecular NLO crystals. These molecular NLO crystals include urea, 2-methyl-4-nitroaniline (MNA), meta-dinotrobenzene (MDNB), 3-methyl-4-methooxy-4^′-nitrostilbene (MMONS), and 3-hydroxyl-4^′-nitrostilbene (HMONS). The calculated results are compared with the measurements and good agreement is found between them. The experimentally unknown values of IR absorption-edges of some new synthesized crystals are predicted. The theoretical analyses of the structural origins of IR absorption cut-offs are discussed. The results are helpful for the molecular simulation and design of potential infrared molecular NLO crystals. Received: 9 April 2002 / Accepted: 18 July 2002 / Published online: 28 October 2002 RID="*" ID="*"Corresponding author. Fax: +86-591/3714946, E-mail: wkc@ms.fjirsm.ac.cn     

<Emphasis Type="Italic">B</Emphasis> and <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">s</Emphasis></Subscript> decay constants from moments of finite energy sum rules in QCD

We use an appropriate combination of moments of finite energy sum rules in QCD in order to compute the B _q -meson decay constants f _B and . We perform the calculation using a two-loop computation of the imaginary part of the pseudoscalar two point function in terms of the running bottom quark mass. The results are stable against the so-called QCD duality threshold, and they are in agreement with the estimates obtained from Borel transform QCD sum rules and lattice computations.Received: 28 July 2004, Revised: 10 September 2004, Published online: 23 November 2004PACS: 12.38.Bx, 12.38.LgSupported by MCYT-FEDER under contract FPA2002-00612.     

Coherent coupling of a single <Superscript>40</Superscript>Ca<Superscript>+</Superscript> ion to a high-finesse optical cavity

We demonstrate coherent coupling of the quadrupole S_1/2D_5/2 optical transition of a single trapped ⁴⁰Ca⁺ ion to the standing wave field of a high-finesse cavity. The dependence of the coupling on temporal dynamics and spatial variations of the intracavity field is investigated in detail. By precisely controlling the position of the ion in the cavity standing wave field and by selectively exciting vibrational state-changing transitions the ion’s quantized vibration in the trap is deterministically coupled to the cavity mode. We confirm coherent interaction of ion and cavity field by exciting Rabi oscillations with short resonant laser pulses injected into the cavity, which is frequency-stabilized to the atomic transition. Received: 23 August 2002 / Published online: 8 January 2003 RID="*" ID="*"Corresponding author. E-mail: christoph.becher@uibk.ac.at RID="**" ID="**"Present address: Time and Frequency Division, National Institute of Standards and Technology, Boulder, CO 80305, USA     

Femtosecond pulsed-laser deposition of BaTiO<Subscript>3</Subscript>

The elemental composition and the surface morphology of thin films grown by laser ablation of barium titanate with femtosecond pulses at 620 nm laser wavelength have been systematically studied according to the experimental pulsed-laser deposition parameters : laser energy density, oxygen pressure, substrate temperature, target–substrate distance and substrate position (in- and off-axis geometry). Firstly, even at high temperature (700 °C), the deposits consist of coalesced particles up to 1-μm in size, mixed in a poorly crystallised tetragonal BaTiO₃ thin film. The particles formed in femtosecond pulsed-laser deposition induce a high surface roughness, which is observed whatever the experimental growth conditions and does not correspond to the droplets often observed during laser ablation in the nanosecond regime. As shown by plasma expansion dynamics, these particles propagate toward the substrate in the plasma plume with a low velocity, and are assumed to be produced by gas-phase reactions. Moreover, the cationic concentration evaluated through the Ba/Ti ratio strongly depends on the oxygen pressure in the ablation chamber and the angular position of the substrate along the normal to the target at laser impact. Indeed, the films appear to be enriched in the heavy element (Ba) when the substrate is located at high angular deviation. This fact is correlated to an increase in the lighter species (i.e. Ti) in the central part of the plasma plume. Received: 30 April 2002 / Accepted: 26 August 2002 / Published online: 8 January 2003 RID="*" ID="*"Corresponding author. Fax: +33-1/4354-2878, E-mail: millon@gps.jussieu.fr RID="**" ID="**"Also at: LSMCL, Université de Metz, 57078 Metz Cedex 3, France     

Maximal atmospheric neutrino mixing in an <Emphasis Type="Italic">SU</Emphasis>(5) model

We show that maximal atmospheric and large solar neutrino mixing can be implemented in SU(5) gauge theories, by making use of the U(1) _F symmetry associated with a suitably defined family number F, together with a Z₂ symmetry which does not commute with F. U(1) _F is softly broken by the mass terms of the right-handed neutrino singlets, which are responsible for the seesaw mechanism; in additio n, U(1) _F is also spontaneously broken at the electroweak scale. In our scenario, lepton mixing stems exclusively from the right-handed-neutrino Majorana mass matrix, whereas the CKM matrix originates solely in the up-type-quark sector. We show that, despite the non-supersymmetric character of our model, unification of the gauge couplings can be achieved at a scale 10¹⁶ GeV < m _U < 10¹⁹ GeV; indeed, we have found a particula r solution to this problem which yields results almost identical to the ones of the minimal supersymmetric standard model. Received: 29 November 2002 / Published online: 3 March 2003 RID="a" ID="a" e-mail: walter.grimus@univie.ac.at RID="b" ID="b" e-mail: balio@cfif.ist.utl.pt     

<Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">K</Emphasis></Subscript> from the lattice with Wilson quarks

We report our results for the bag parameter B _K obtained from the quenched simulations on the lattice with Wilson fermions for three values of the lattice spacing. We implemented the method by which no subtraction of the mixing with other four-fermion operators is needed. Our final result, in terms of the renormalization group invariant bag parameter, is .Received: 9 July 2004, Revised: 27 July 2004, Published online: 21 September 2004     

Passive Advection and the Degenerate Elliptic Operators <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>

 We prove estimates for the stationary state n-point functions at zero molecular diffusivity in the Kraichnan model [13]. This is done by proving upper bounds for the heat kernels and Green's functions of the degenerate elliptic operators M _n that occur in the Hopf equations for the n-point functions. Received: 25 August 2001 / Accepted: 30 September 2002 Published online: 20 January 2003 Communicated by A. Kupiainen     

Proton spin structure function,g<Subscript>1</Subscript>, with the unified evolution equations including NLO DGLAP terms and double logarithms, <Emphasis Type="Italic">ln</Emphasis>(1/<Emphasis Type="Italic">x</Emphasis>)

Theoretical predictions show that at low values of the Bjorken parameter x the spin structure function, g₁, is influenced by large logarithmic corrections, , which may be predominant in this region. These corrections are also partially contained in the NLO part of the standard DGLAP evolution. Here we calculate the nucleon structure function, g₁, and the gluon distribution, , using the unified evolution equations written for the singlet and the non-singlet parton distributions. These equations include (i) the terms which describe the NLO DGLAP evolution and (ii) the ladder and non-ladder terms which contribute to the resummation of . Subtractions of singularities from the evolution kernels are performed so as to avoid double counting the double logarithmic contributions coming from the NLO DGLAP and the ladder and non-ladder terms. The sensitivity of the results to the factorization scheme applied is tested by introducing the DGLAP terms into the evolution equations at two different factorization schemes. Received: 30 January 2003 / Published online: 5 May 2003 RID="a" ID="a" e-mail: ziaja@unix.tsl.uu.se     

Comparative investigation of <Emphasis Type="Bold">39</Emphasis>K and <Emphasis Type="Bold">40</Emphasis>K trap loss rates: alternative loss channel at low light intensities

We report a comparative investigation of trap loss rates in a magneto-optical trap for two potassium isotopes, ³⁹K and ⁴⁰K, as a function of trap light intensity. The isotopes present a quite similar behavior for the loss rates at high intensities, and a sudden increase of the loss rates at low intensities is present in both cases. While for ³⁹K such increase can be explained assuming that the major contribution to the losses comes from hyperfine changing collisions, a different loss mechanism must be considered for ⁴⁰K, which has an inverted ground state hyperfine structure. The experimental results of both isotopes are well reproduced by an alternative model based on radiative escape as the dominant loss mechanism. Received 1st May 2002 / Received in final form 19 October 2002 Published online 4 March 2003 RID="a" ID="a"Alternative address: Dipartimento di Fisica, Universitá di Trento, 38050 Povo (Tn), Italy. RID="b" ID="b"e-mail: marcassa@if.sc.usp.br     

A Class of Integrable Spin Calogero-Moser Systems

 We introduce a class of spin Calogero-Moser systems associated with root systems of simple Lie algebras and give the associated Lax representations (with spectral parameter) and fundamental Poisson bracket relations. The associated integrable models (called integrable spin Calogero-Moser systems in the paper) and their Lax pairs are then obtained via Poisson reduction and gauge transformations. For Lie algebras of A _n -type, this new class of integrable systems includes the usual Calogero-Moser systems as subsystems. Our method is guided by a general framework which we develop here using dynamical Lie algebroids. Received: 19 October 2001 / Accepted: 7 June 2002 Published online: 21 October 2002 RID="*" ID="*" Research partially supported by NSF grant DMS00-72171.     

Electron-electron bound states in Maxwell-Chern-Simons-Proca QED <Emphasis Type="Bold">3</Emphasis>

We start from a parity-breaking MCS QED₃ model with spontaneous breaking of the gauge symmetry as a framework for evaluation of the electron-electron interaction potential and for attainment of numerical values for the e ^- e ^- - bound state. Three expressions ( V _eff , V _eff , V _eff ) are obtained according to the polarization state of the scattered electrons. In an energy scale compatible with condensed matter electronic excitations, these three potentials become degenerated. The resulting potential is implemented in the Schr?dinger equation and the variational method is applied to carry out the electronic binding energy. The resulting binding energies in the scale of 10-100 meV and a correlation length in the scale of 10-30 ? are possible indications that the MCS-QED₃ model adopted may be suitable to address an eventual case of e ^- e ^- pairing in the presence of parity-symmetry breakdown. The data analyzed here suggest an energy scale of 10-100 meV to fix the breaking of the U (1)-symmetry. Received 24 September 2002 / Received in final form 15 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: belich@cbpf.br RID="b" ID="b"e-mail: delcima@cbpf.br RID="c" ID="c"e-mail: manojr@cbpf.br RID="d" ID="d"e-mail: helayel@cbpf.br     

The <Emphasis Type="Italic">N</Emphasis> = <Emphasis Type="Italic">Z</Emphasis><Emphasis Type="Italic">f</Emphasis><Subscript>7/2</Subscript>-shell nuclei: Experimental highlights

During the last decade, as the experimental and computing means and techniques have rapidly evolved, the experimental investigation of the f_7/2-shell nuclei has gained renewed interest. TheN = Z nuclei studied with the GASP array range from ⁴⁴Ti to ⁵²Fe. The results extended the knowledge of their structure up to high spins and excitation energies, above band terminations, where the competition with the charged-particles emission was initially thought to obscure the possibility of gamma-ray spectroscopy investigation. The paper highlights some of the most outstanding properties of these nuclei such as the nuclear rotation and backbending effects, band termination states, yrast traps, non-natural parity bands, competition between T = 0 and T = 1 pn pairing modes.Received: 30 October 2002, Published online: 16 March 2004PACS: 21.10.-k Properties of nuclei; nuclear energy levels - 21.60.Cs Shell model - 23.20.Lv transitions and level energies - 27.40. + z C.A. Ur: On leave from NIPNE Bucharest, Romania