A BGG-Type Resolution for Tensor Modules over General Linear Superalgebra

We construct a Bernstein–Gelfand–Gelfand type resolution in terms of direct sums of Kac modules for the finite-dimensional irreducible tensor representations of the general linear superalgebra. As a consequence it follows that the unique maximal submodule of a corresponding reducible Kac module is generated by its proper singular vector. Ngau Lam was partially supported by an NSC-grant 96-2115-M-006-008-MY3 of the ROC.     

Novel technique for the measurement of fiber dispersion properties

We present a novel method for measuring the linear and nonlinear dispersion properties of conventional and micro-structured fibers. It is based on the automated compensation of phase modulations using a high-resolution pulse-shaping device. No tunable laser source is required. Received: 20 December 2002 / Published online: 19 March 2003 RID="*" ID="*"Corresponding author. Fax: +49-3641/947202, E-mail: stobrawa@ioq.uni-jena.de RID="**" ID="**"Present address: Carl Zeiss Meditec AG, G?schwitzer Strasse 51–52, 07745 Jena, Germany     

Quantitative laser-induced fluorescence of CH in atmospheric pressure flames

/ Published online: 11 June 2003 RID="*" ID="*"Present address: Lam Research Corporation, Fremont, CA 94538, USA RID="**" ID="**"Present address: Mechanical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands RID="***" ID="***"Present address: Mechanical Engineering Dept., Stanford University, Stanford CA 94305, USA RID="****" ID="****"Corresponding author. Fax: +1-650/859-6196, E-mail: smith@mplvax.sri.com     

Characterization of nonlinear optical parameters of polymethine dyes

We investigated nonlinear refraction, nonlinear absorption, and saturable absorption of polymethine dyes by the Z-scan technique (λ=1064 nm). The analysis of simultaneous appearance of several nonlinear optical processes in dye solutions excited by picosecond pulses was carried out. The saturable absorption was analyzed taking into account various models. Nonlinear refractive indices, nonlinear absorption coefficients, and saturation intensities of various polymethine dyes were measured. Received: 27 December 2002 / Revised version: 6 March 2003 / Published online: 5 May 2003 RID="*" ID="*"Corresponding author. Fax: +81-471/363-366, E-mail: r_ganeev@issp.u-tokyo.ac.jp RID="**" ID="**"Present address: The Institute for Solid State Physics, The Tokyo University, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8581, Japan     

Phonon–phonon interactions due to non-linear effects in a linear ion trap

We examine in detail the theory of the intrinsic non-linearities in the dynamics of trapped ions due to the Coulomb interaction. In particular, the possibility of mode–mode coupling, which can be a source of decoherence in trapped ion quantum computation, or can be exploited for parametric down-conversion of phonons, is discussed and conditions under which such coupling is possible are derived. Received: 8 November 2002 / Published online: 26 March 2003 RID="*" ID="*"Permanent address: MIP, Université Pierre et Marie Curie and Département de Physique, école Normale Supérieure, 75005 Paris, France RID="**" ID="**"Corresponding author. Fax: +1-505/667-1931, E-mail: dfvj@lanl.gov     

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.     

Banach Lie-Poisson Spaces and Reduction

 We investigate the long-time behavior of the Glauber dynamics for the random energy model below the critical temperature. We establish that for a suitably chosen timescale that diverges with the size of the system, one can prove that a natural autocorrelation function exhibits aging. Moreover, we show that the long-time asymptotics of this function coincide with those of the so-called ``REM-like trap model' proposed by Bouchaud and Dean. Our results rely on very precise estimates on the distribution of transition times of the process between different states of extremely low energy. Received: 9 October 2001 / Accepted: 17 October 2002 Published online: 21 March 2003 RID="*" ID="*" Work Partially supported by the Swiss National Science Foundation under contract 21-65267.01 RID="**" ID="**" On leave from CPT-CNRS, Luminy, Case 907, 13288 Marseille Cedex 9, France. E-mail: veronique.gayrard@epfl.ch Communicated by M. Aizenman     

On the Sutherland Spin Model of <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">N</Emphasis></Subscript> Type and Its Associated Spin Chain

 The B _N hyperbolic Sutherland spin model is expressed in terms of a suitable set of commuting Dunkl operators. This fact is exploited to derive a complete family of commuting integrals of motion of the model, thus establishing its integrability. The Dunkl operators are shown to possess a common flag of invariant finite-dimensional linear spaces of smooth scalar functions. This implies that the Hamiltonian of the model preserves a corresponding flag of smooth spin functions. The discrete spectrum of the restriction of the Hamiltonian to this spin flag is explicitly computed by triangularization. The integrability of the hyperbolic Sutherland spin chain of B _N type associated with the dynamical model is proved using Polychronakos's ``freezing trick'. Received: 14 February 2002 / Accepted: 19 June 2002 Published online: 10 December 2002 RID="*" ID="*" Corresponding author. E-mail: artemio@fis.ucm.es RID="**" ID="**" On leave of absence from Institute of Mathematics, 3 Tereschenkivska St., 01601 Kyiv-4 Ukraine Communicated by L. Takhtajan     

Potts Model on Infinite Graphs and the Limit of Chromatic Polynomials

 Given an infinite graph 𝔾 quasi-transitive and amenable with maximum degree Δ, we show that reduced ground state degeneracy per site W _r (𝔾, q) of the q-state antiferromagnetic Potts model at zero temperature on 𝔾 is analytic in the variable 1/q, whenever |2Δe ³ /q|<1. This result proves, in an even stronger formulation, a conjecture originally sketched in [12] and explicitly formulated in [16 and 19], based on which a sufficient condition for W _r (𝔾, q) to be analytic at 1/q=0 is that 𝔾 is a regular lattice. Received: 16 January 2002 / Accepted: 17 October 2002 Published online: 18 February 2003 RID="*" ID="*" Partially supported by CNPq (Brazil) RID="**" ID="**" Partially supported by CNR, G.N.F.M. (Italy) Communicated by H. Spohn     

Ion irradiation of exchange bias systems for magnetic sensor applications

It has been demonstrated that He⁺ ion irradiation is an excellent tool for modifying magnetic properties, like the magnetic anisotropy, the interlayer exchange coupling strength and the exchange bias field of ultra-thin magnetic layered systems. This paper summarizes the effects of ion irradiation on exchange bias systems. As a first example, for possible applications of the ion induced magnetic effects, the realization of an angle sensing device is described. Received: 11 November 2002 / Accepted: 12 November 2002 / Published online: 4 April 2003 RID="*" ID="*"Corresponding author. Fax: +49-631-205-4095, E-mail: fassbend@physik.uni-kl.de RID="**" ID="**"Present address: Université de Rouen, Rouen, France     

Studies of high-repetition-rate laser plasma EUV sources from droplet targets

The water droplet laser plasma source has been shown to have many attractive features as a continuous, almost debris-free source for extreme ultraviolet (EUV) and X-ray applications. Through a dual experimental and theoretical study, we analyze the interaction physics between the laser light and the target. The hydrodynamic laser plasma simulation code, Medusa103 is used to model the electron density distribution for comparison to electron density distributions obtained through Abel inversion of plasma interferograms. In addition, flat field EUV spectra are compared to synthetic spectra calculated with the atomic physics code RATION. Received: 31 October 2002 / Accepted: 8 February 2003 / Published online: 28 May 2003 RID="*" ID="*"Present address: Naval Reseach Laboratory, Washington D.C. RID="**" ID="**"Present address: Xtreme Technologies, G?ttingen, Germany. RID="***" ID="***"Corresponding author. Fax: +1-407/823-3570, E-mail: mrichard@mail.ucf.edu     

Sub-nanosecond microchip laser with intracavity Raman conversion

Efficient sub-nanosecond pulse operation of microchip lasers with intracavity Raman conversion and pulse compression is presented for the first time. The microchip lasers were composed of Nd:LSB or Nd:YAG laser crystals, Cr⁴⁺:YAG saturable absorber, and Ba(NO₃)₂ Raman medium. The pulse duration obtained at the Stokes wavelength (1196 nm) was as short as 118 ps. Optical conversion efficiency of laser-diode pump power to the Stokes power of 8% was reached. Pulse energy and peak power of Stokes emission were 1.2 μJ and 5.4 kW, correspondingly. Numerical calculations are in good agreement with obtained experimental results. Received: 20 December 2002 / Revised version: 6 March 2003 / Published online: 5 May 2003 RID="*" ID="*"Corresponding author. Fax: +1-716/645-6945, E-mail: ankuzmin@acsu.buffalo.edu RID="**" ID="**"Present address: University at Buffalo, SUNY, The Institute for Lasers, Photonics, and Biophotonics, 458 NSC, Buffalo, NY 14 260-3000, USA     

The application of quasi-phase-matched parametric light sources to practical infrared chemical sensing systems

Quasi-phase-matched (QPM) materials allow the generation of spectroscopically useful infrared radiation in an efficient and broadly tunable format. Here, we describe several applications of QPM-based light sources to remote and local chemical sensing. The remote systems are gas imagers that employ a fiber-pumped continuous-wave optical parametric oscillator or a microlaser-pumped, diode-seeded optical parametric amplifier as the illumination source. Technology described for local sensing includes a cavity ring down spectrometer that employs a novel optical parametric generator–amplifier to achieve ≥350 cm^-1 of contiguous tuning and a long-wave infrared light source based on QPM GaAs. In each case the use of QPM materials in conjunction with effective pump sources instills simplicity and ruggedness into the sensing systems. Received: 15 April 2002 / Revised version: 6 June 2002 / Published online: 12 September 2002 RID="*" ID="*"Corresponding author. Fax: +1-925/294-2595, E-mail: tjkulp@sandia.gov RID="**" ID="**"Present address: Corning Inc., Corning, NY 14831, USA RID="*" ID="*"Present address: Corning Inc., Corning, NY 14831, USA RID="**" ID="**"Present address: Blue Leaf Networks, Sunnyvale, CA 94086, USA RID="***" ID="***"Present address: Sandia National Laboratories, Albuquerque, NM 87185, USA     

Diffusion of Ta in α-Ti

The diffusion of Ta in the hcp (α) phase of high-purity Ti (99.99%) was studied at different temperatures from 911 K up to 1123 K. The Rutherford Backscattering Spectrometry (RBS) and Heavy Ion RBS (HIRBS) techniques were used to obtain the penetration profiles. The evolution of the diffusion coefficient, D, as a function of temperature follows prediction of the Arrhenius law. The activation energy of the diffusion process is (318±7)kJ/mol, similar to that corresponding to self-diffusion in α-Ti. On the other hand, the measured values of D are systematically lower than those corresponding to self-diffusion by a factor of approximately 5. This reduction could be explained by taking into account the mass difference between Ta and Ti. An increase of the diffusion coefficient was measured when the diffusion proceeds on a less pure Ti (99.9%) matrix. This increment is higher at lower temperatures. Received: 12 November 2001 / Accepted: 12 March 2002 / Published online: 5 July 2002 RID="*" ID="*" RID="*" ID="*" RID="**" ID="**"Corresponding author. Fax: +54-11/6772-7362, E-mail: dyment@cnea.gov.ar RID="*" ID="*"Members of the Carrera del Investigador Científico del Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina     

Hitchin Systems – Symplectic Hecke Correspondence and Two-Dimensional Version

 The aim of this paper is two-fold. First, we define symplectic maps between Hitchin systems related to holomorphic bundles of different degrees. We call these maps the Symplectic Hecke Correspondence (SHC) of the corresponding Higgs bundles. They are constructed by means of the modification of the underlying holomorphic bundles. SHC allows to construct B?cklund transformations in the Hitchin systems defined over Riemann curves with marked points. We apply the general scheme to the elliptic Calogero-Moser (CM) system and construct SHC to an integrable SL(N,ℂ) Euler-Arnold top (the elliptic SL(N,ℂ)-rotator). Next, we propose a generalization of the Hitchin approach to 2d integrable theories related to the Higgs bundles of infinite rank. The main example is an integrable two-dimensional version of the two-body elliptic CM system. The previous construction allows us to define SHC between the two-dimensional elliptic CM system and the Landau-Lifshitz equation. Received: 19 April 2002 / Accepted: 14 November 2002 Published online: 18 February 2003 RID="*" ID="*" On leave from Institute of Oceanology, Moscow, Russia RID="**" ID="**" On leave from Institute of Theoretical and Experimental Physics, Moscow, Russia Communicated by L. Takhtajan     

Decay Rates and Probability Estimates¶for Massive Dirac Particles¶in the Kerr–Newman Black Hole Geometry

The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr–Newman geometry, for smooth initial data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays in at least at the rate t ^−5/6. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p = 0, 1 or 0 < p < 1. The proofs are based on a refined analysis of the Dirac propagator constructed in [4]. Received: 20 August 2001 / Accepted: 22 January 2002 RID="*" ID="*"Present address: NWF I – Mathematik, Universit?t Regensburg, 93040 Regensburg, Germany.?E-mail: felix.finster@mathematik.uni-regensburg.de RID="**" ID="**"Research supported by NSERC grant # RGPIN 105490-1998. RID="***" ID="***"Research supported in part by the NSF, Grant No. DMS-0103998. RID="****" ID="****"Research supported in part by the NSF, Grant No. 33-585-7510-2-30.     

Quantum Spheres and Projective Spaces as Graph Algebras

 The C ^* -algebras of continuous functions on quantum spheres, quantum real projective spaces, and quantum complex projective spaces are realized as Cuntz-Krieger algebras corresponding to suitable directed graphs. Structural results about these quantum spaces, especially about their ideals and K-theory, are then derived from the general theory of graph algebras. It is shown that the quantum even and odd dimensional spheres are produced by repeated application of a quantum double suspension to two points and the circle, respectively. Received: 31 January 2001 / Accepted: 29 July 2002 Published online: 7 November 2002 RID="*" ID="*" Supported by grant No. R04–2001–000–00117–0 from the Korea Science & Engineering Foundation. RID="**" ID="**" Partially supported by the Research Management Committee of the University of Newcastle.     

Dynamic temporal pulse shaping in advanced ultrafast laser material processing

Phase-manipulated ultrafast laser pulses and temporally tailored pulse trains with THz repetition rates are promising new tools for quality micromachining of brittle dielectrics, allowing to adapt the laser energy delivery rate to the material properties for optimal processing. Different materials respond with specific reaction pathways to the sudden energy input depending on the efficiency of electron generation and on the ability to release the energy into the lattice. The sequential energy delivery with judiciously chosen pulse trains may induce softening of the material during the initial steps of excitation and change the energy coupling for the subsequent steps. We show that this can result in lower stress, cleaner structures, and allow for a material-dependent optimization process. Received: 7 October 2002 / Accepted: 20 January 2003 / Published online: 28 May 2003 RID="*" ID="*"Corresponding author. Fax: +49-30/6392-1229, E-mail: stoian@mbi-berlin.de RID="**" ID="**"Now at Katana Technologies GmbH, Albert-Einstein-Ring 7, 14532 Kleinmachnow, Germany     

Finite-Dimensional Half-Integer Weight Modules over Queer Lie Superalgebras

We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra \({\mathfrak{q}(n)}\). It is given in terms of the Brundan’s work on finite-dimensional integer weight \({\mathfrak{q}(n)}\)-modules by means of Lusztig’s canonical basis. Using this viewpoint we compute the characters of the finite-dimensional half-integer weight irreducible modules. For a large class of irreducible modules whose highest weights are of special types (i.e., totally connected or totally disconnected) we derive closed-form character formulas that are reminiscent of the Kac–Wakimoto character formula for basic Lie superalgebras.     

Transmission and scanning electron microscopy studies of single femtosecond- laser-pulse ablation of silicon

The final state of the material resulting from laser irradiation of silicon using 130 fs pulses at 790 nm was studied using a number of techniques including scanning and transmission electron microscopies, as well as atomic force microscopy. Structural details and the level of damage to the nearby solid following irradiation were characterized and are discussed in the context of recent dynamical studies. Received: 28 September 2001 / Accepted: 3 March 2002 / Published online: 19 July 2002 RID="*" ID="*"Department of Engineering Physics, McMaster University, Hamilton, Ontario, L8S 4M1, Canada RID="**" ID="**"Corresponding author. Fax: +1-905/521-2773, E-mail: borowia@mcmaster.ca RID="***" ID="***"Present address: Department of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ, UK RID="****" ID="****"Department of Materials Science and the CEMD, McMaster University, Hamilton, Ontario, L8S 4M1, Canada RID="*****" ID="*****"Departments of Engineering Physics, and Physics and Astronomy, and the CEMD, McMaster University, Hamilton, Ontario, L8S 4M1, Canada