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.     

Rationality, Quasirationality and Finite W-Algebras

 Some of the consequences that follow from the C ₂ condition of Zhu are analysed. In particular it is shown that every conformal field theory satisfying the C ₂ condition has only finitely many n-point functions, and this result is used to prove a version of a conjecture of Nahm, namely that every representation of such a conformal field theory is quasirational. We also show that every such vertex operator algebra is a finite W-algebra, and we give a direct proof of the convergence of its characters as well as the finiteness of the fusion rules. Received: 18 October 2000 / Accepted: 28 January 2003 Published online: 5 May 2003 RID="*" ID="*" Present address: Department of Mathematics, King's College London, Strand, London WC2R 2LS, U.K. E-mail: mrg@mth.kcl.ac.uk RID="**" ID="**" Present address: Harvard University, Department of Mathematics, One Oxford Street, Cambridge, MA 02138, USA. E-mail: aneitzke@alumni.princeton.edu Communicated by R.H. Dijkgraaf     

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     

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     

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     

Linear Stability in an Ideal Incompressible Fluid

 We give an explicit construction of approximate eigenfunctions for a linearized Euler operator in dimensions two and three with periodic boundary conditions, and an estimate from below for its spectral bound in terms of an appropriate Lyapunov exponent. As a consequence, we prove that in dimension 2 the spectral and growth bounds for the corresponding group are equal. Therefore, the linear hydrodynamic stability of a steady state for the Euler equations in dimension 2 is equivalent to the fact that the spectrum of the linearized operator is pure imaginary. In dimension 3 we prove the estimate from below for the spectral bound that implies the same equality for every example where the relevant Lyapunov exponents could be effectively computed. For the kinematic dynamo operator describing the evolution of a magnetic field in an ideally conducting incompressible fluid we prove that the growth bound equals the spectral bound in dimensions 2 and 3. Received: 20 May 2002 / Accepted: 5 September 2002 Published online: 10 January 2003 RID="*" ID="*" The first author was partially supported by the Twinning Program of the National Academy of Sciences and National Science Foundation, and by the Research Council and Research Board of the University of Missouri. RID="**" ID="**" The second author was partially supported by the National Science Foundation grant DMS 9876947 and CRDF grant RM1-2084. Acknowledgements. The authors thank Susan Friedlander for useful discussions. Communicated by P. Constantin     

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     

Infinite-Dimensional Lie Superalgebras and Hook Schur Functions

 Making use of a Howe duality involving the infinite-dimensional Lie superalgebra and the finite-dimensional group GL _l of [CW3] we derive a character formula for a certain class of irreducible quasi-finite representations of in terms of hook Schur functions. We use the reduction procedure of to to derive a character formula for a certain class of level 1 highest weight irreducible representations of, the affine Lie superalgebra associated to the finite-dimensional Lie superalgebra . These modules turn out to form the complete set of integrable -modules of level 1. We also show that the characters of all integrable level 1 highest weight irreducible -modules may be written as a sum of products of hook Schur functions. Received: 6 March 2002 / Accepted: 15 January 2003 Published online: 14 March 2003 RID="*" ID="*" Partially supported by NSC-grant 91-2115-M-002-007 of the R.O.C. RID="**" ID="**" Partially supported by NSC-grant 90-2115-M-006-015 of the R.O.C. Communicated by M. Aizenman     

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     

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     

Exciton dispersion in silicon nanostructures formed by intense,ultra-fast electronic excitation

The intense, ultra-fast electronic excitation of clean silicon (100)–(2×1) surfaces leads to the formation of silicon nanostructures embedded in silicon, which photoluminesce in the yellow-green (∼2-eV band gap). The silicon surfaces were irradiated with slow, highly charged ions (e.g. Xe⁴⁴⁺ and Au⁵³⁺) to produce the ultra-fast electronic excitation. The observation of excitonic features in the luminescence from these nanostructures has recently been reported. In this paper we report the dispersion of the excitonic features with laser excitation energy. A phonon-scattering process is proposed to explain the observed dispersion. Received: 2 October 2001 / Accepted: 18 July 2002 / Published online: 25 October 2002 RID="*" ID="*"Corresponding author. Fax: +1-925/423-7040, E-mail: Hamza1@llnl.gov RID="**" ID="**"Present address: University of California, Lawrence Berkeley National Laboratory, Berkeley, CA 94 720, USA     

Mid-infrared polarization spectroscopy of carbon dioxide

The use of mid-infrared polarization spectroscopy (PS) for the detection of CO₂ has been demonstrated. The P(13) and P(14) resonances of the (0 0⁰ 0)→(1 0⁰ 1) transition of CO₂ were probed using a single-mode optical parametric generator system to produce a high-intensity laser beam at approximately 2.7 μm. The experiments were performed in an atmospheric pressure CO₂ jet and also in a sub-atmospheric pressure gas cell. The experimental results were compared with the results of the time-dependent density-matrix equations using direct numerical integration. The Zeeman-state structure of the upper and lower energy levels was included in the multi-state formulation of the density-matrix equations. Fifty-eight Zeeman states and two bath levels were included in the numerical analysis of the P(14) transition. The measured and calculated PS line shapes were in good agreement, and the absolute experimental signal level agreed with the theoretical calculation to within a factor of five. Received: 20 March 2002 / Revised version: 16 August 2002 / Published online: 11 December 2002 RID="*" ID="*"Present address: Innovative Scientific Solutions Inc., 2766 Indian Ripple Road, Dayton, OH 45 440, USA RID="**" ID="**"Corresponding author. Fax: +1-765/494-0539, E-mail: Lucht@purdue.edu RID="***" ID="***"Present address: School of Mechanical Engineering, Purdue University, W. Lafayette, IN 47807-2040 USA     

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     

Laser transitions under resonant optical pumping of donor centres in Si:P

Terahertz stimulated emission of phosphorus donors in silicon optically excited by radiation from the free-electron laser FELIX has been studied. It is found that a spectral line of the Si:P laser emission depends on pump frequency. Stimulated emission arises on the 2p₀→1s(E) intra-centre transition (21.2 meV) under resonant pumping of the 2p₀ state and on the 2p₀→1s(T₂) transition (22.3 meV) under pumping of the 2p_± or higher odd-parity donor states. The line shift is attributed to the Auger redistribution of the 1s(E)- and 1s(T₂)-state populations. Received: 7 November 2002 / Revised version: 7 April 2003 / Published online: 14 May 2003 RID="*" ID="*"Corresponding author. Fax: +49-30/6705-55-07, E-mail: sergeij.pavlov@dlr.de RID="**" ID="**"On leave from: The Institute for Physics of Microstructures, Nizhny Novgorod, Russia     

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     

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     

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     

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     

Removal of oxygen atoms from a SiO2 surface by incoherent vacuum ultraviolet excimer irradiation

We have demonstrated the non-thermal removal of oxygen atoms from an oxidized silicon surface (SiO₂) on a silicon wafer by the use of a low-power (0.3 mW cm^-2) incoherent vacuum ultraviolet (VUV) light source at 126 nm. X-ray photoelectron spectroscopy (XPS) has shown that a maximum Si concentration of 80% appears at the surface after a 20-h irradiation with 9.8 eV photons, as a result of oxygen removal from the SiO₂ matrix. The surface morphology, however, indicates no damage or melting on the surface even after the irradiation. Received: 15 April 2002 / Accepted: 17 April 2002 / Published online: 10 September 2002 RID="*" ID="*"Permanent address: Nano-Tech Photon Inc., Shimotomita 4132-1, Shintomi, Miyazaki, 889-1404, Japan RID="**" ID="**"Corresponding author. Fax: +81-985/583-899, E-mail: kubodera@opt.miyazaki-u.jp