Density of States for Random Band Matrices

 By applying the supersymmetric approach we rigorously prove smoothness of the averaged density of states for a three dimensional random band matrix ensemble, in the limit of infinite volume and fixed band width. We also prove that the resulting expression for the density of states coincides with the Wigner semicircle with a precision 1/W ² , for W large but fixed. Received: 6 February 2002 / Accepted: 17 July 2002 Published online: 7 November 2002 RID="*" ID="*" Supported by NSF grant DMS 9729992     

Electrical switching studies on As<Subscript>40</Subscript>Te<Subscript>60-x</Subscript>Se<Subscript>x</Subscript> and As<Subscript>35</Subscript>Te<Subscript>65-x</Subscript>Se<Subscript>x</Subscript> glasses

The I–V characteristics of bulk As₄₀Te_60-xSe_x and As₃₅Te_65-xSe_x glasses have been studied with a current sweep of 0–18 mA-0, over a wide range of compositions (4≤x≤22). All the glasses studied showed a threshold electrical switching behaviour. The number of switching cycles withstood by the samples has been found to depend on the ON-state current. It is seen that the switching voltages increase with increase in selenium content. Further, the switching voltages are found to be almost independent of the thickness of the sample (d), in the range 0.18–0.3 mm. Also, the switching voltages and the number of switching cycles withstood by the samples are found to decrease with temperature. Received: 6 November 2002 / Accepted: 8 November 2002 / Published online: 29 January 2003 RID="*" ID="*"Corresponding author. Fax: +91-80/360-0135, E-mail: sasokan@isu.iisc.ernet.in     

Structure,transport and field-emission properties of compound nanotubes: CN<Subscript>x</Subscript> vs. BNC<Subscript>x</Subscript> (<Emphasis Type="Italic">x</Emphasis><0.1)

Transport and field-emission properties of as-synthesized CN_x and BNC_x (x<0.1) multi-walled nanotubes were compared in detail. Individual ropes made of these nanotubes and macrofilms of those were tested. Before measurements, the nanotubes were thoroughly characterized using high-resolution and energy-filtered electron microscopy, electron diffraction and electron-energy-loss spectroscopy. Individual ropes composed of dozens of CN_x nanotubes displayed well-defined metallic behavior and low resistivities of ∼10–100 kΩ or less at room temperature, whereas those made of BNC_x nanotubes exhibited semiconducting properties and high resistivities of ∼50–300 MΩ. Both types of ropes revealed good field-emission properties with emitting currents per rope reaching ∼4 μA(CN_x) and ∼2 μA (BNC_x), albeit the latter ropes se- verely deteriorated during the field emission. Macrofilms made of randomly oriented CN_x or BNC_x nanotubes displayed low and similar turn-on fields of ∼2–3 V/μm. 3 mA/cm² (BNC_x) and 5.5 mA/cm² (CN_x) current densities were reached at 5.5 V/μm macroscopic fields. At a current density of 0.2–0.4 mA/cm² both types of compound nanotubes exhibited equally good emission stability over tens of minutes; by contrast, on increasing the current density to 0.2–0.4 A/cm², only CN_x films continued to emit steadily, while the field emission from BNC_x nanotube films was prone to fast degradation within several tens of seconds, likely due to arcing and/or resistive heating. Received: 29 October 2002 / Accepted: 1 November 2002 / Published online: 10 March 2003 RID="*" ID="*"Corresponding author. Fax: +81-298/51-6280, E-mail: golberg.dmitri@nims.go.jp     

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.     

Large-scale synthesis of crystalline β-SiC nanowires

Large quantities of high-purity crystalline β-SiC nanowires have been synthesized at relatively low temperature via a new simple method, the chemical-vapor-reaction approach, in a home-made graphite reaction cell. A mixture of milled Si and SiC powders and C₃H₆ were employed as the starting materials. The results show that the nanowires with diameters of about 10–35 nm are single crystalline β-SiCwithout any wrapping of amorphous material, and the nanowire axes lie along the 〈111〉 direction. Some unique properties are found in the Raman scattering from the β-SiC nanowires, which are different from previous observations of β-SiC materials. A possible growth mechanism for the β-SiC nanowires is proposed. Received: 27 August 2002 / Accepted: 28 August 2002 / Published online: 4 December 2002 RID="*" ID="*"Corresponding author. Fax: +86-29/8491-000, E-mail: zjli-sohu@sohu.com     

Oxygen plasma and high pressure H<Subscript>2</Subscript>O vapor heat treatments used to fabricate polycrystalline silicon thin film transistors

Oxygen plasma and high pressure H₂O vapor heat treatment were applied to fabrication of n-channel polycrystalline silicon thin film transistors (poly-Si TFTs). 13.56 MHz-oxygen-plasma treatment at 250 °C, 100 W for 5 min effectively reduced defect states of 25-nm-thick silicon films crystallized by 30 ns-pulsed XeCl excimer laser irradiation. 1.3×10⁶-Pa-H₂O vapor heat treatment at 260 °C for 3 h was carried out in order to improve electrical properties of SiO_x gate insulators and SiO_x/Si interfaces. A carrier mobility of 470 cm²/V s and a low threshold voltage of 1.8 V were achieved for TFTs fabricated with crystallization at 285 mJ/cm². Received: 18 November 2002 / Accepted: 25 November 2002 / Published online: 11 April 2003 RID="*" ID="*"Corresponding author. Fax: +81-42/388-7109, E-mail: tsamesim@cc.tuat.ac.jp     

N+BF<Subscript>2</Subscript> and N+C+BF<Subscript>2</Subscript> high-dose co-implantation in silicon

Nitrogen and boron BF₂, and nitrogen, carbon, and boron BF₂ high-dose (6×10¹⁶–3×10¹⁷ cm^-2) co-implantation were performed at energies of about 21–77 keV. Subsequent high-temperature annealing processes (600, 850, and 1200 °C) lead to the formation of three and two surface layers respectively. The outer layer mainly consists of polycrystalline silicon and some amorphous material and Si₃N₄ inclusions. The inner layer is highly defective crystalline silicon, with some inclusions of Si₃N₄ too. In the N+B-implanted sample the intermediate layer is amorphous. Co-implantation of boron with nitrogen and with nitrogen and carbon prevents the excessive diffusivity of B and leads to a lattice-parameter reduction of 0.7–1.0%. Received: 10 January 2002 / Accepted: 30 May 2002 / Published online: 4 November 2002 RID="*" ID="*"Corresponding author. Fax: +34-91/3974895; E-mail: Lucia.Barbadillo@uam.es     

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     

Wavelength-agile fiber laser using group-velocity dispersion of pulsed super-continua and application to broadband absorption spectroscopy

A swept-wavelength source is created by connecting four elements in series: a femtosecond fiber laser at 1.56 μm, a non-linear fiber, a dispersive fiber and a tunable spectral bandpass filter. The 1.56-μm pulses are converted to super-continuum (1.1–2.2 μm) pulses by the non-linear fiber, and these broadband pulses are stretched and arranged into wavelength scans by the dispersive fiber. The tunable bandpass filter is used to select a portion of the super-continuum as a scan-wavelength output. A variety of scan characteristics are possible using this approach. As an example, an output with an effective linewidth of approximately 1 cm^-1 is scanned from 1350–1550 nm every 20 ns. Compared to previous scanning benchmarks of approximately 1 nm/μs, such broad, rapid scans offer new capabilities: a gas sensing application is demonstrated by monitoring absorption bands of H₂O, CO₂, C₂H₂ and C₂H₆O at a pressure of 10 bar. Received: 5 August 2002 / Revised version: 23 September 2002 / Published online: 22 November 2002 RID="*" ID="*"Corresponding author. Fax: +1-608/265-2316, E-mail: ssanders@engr.wisc.edu     

Synthesis and photoluminescence of aligned SiO<Subscript>x</Subscript> nanowire arrays

Aligned SiO_x nanowire arrays standing on a Si substrate were successfully synthesized using a simple method by heating a single-crystalline Si slice covered with SiO₂ nanoparticles at 1000 °C in a flowing Ar atmosphere. The SiO_x nanowire arrays were characterized by scanning electron microscopy and transmission electron microscopy. The SiO_x nanowires become progressively thinner from bottom to top. The formation process of the SiO_x nanowire arrays is closely related to a vapor–solid mechanism. Room-temperature photoluminescence measurements under excitation at 260 nm showed that the SiO_x nanowire arrays had a strong blue–green emission at 500 nm (about 2.5 eV), which may be related to oxygen defects. Received: 29 April 2002 / Accepted: 30 April 2002 / Published online: 10 September 2002 RID="*" ID="*"Corresponding author. Fax: +86-551-559-1434, E-mail: gwmeng@mail.issp.ac.cn     

Einstein Relation for a Class of Interface Models

 A class of SOS interface models which can be seen as simplified stochastic Ising model interfaces is studied. In the absence of an external field the long-time fluctuations of the interface are shown to behave as Brownian motion with diffusion coefficient given by a Green-Kubo formula. When a small external field h is applied, it is shown that the shape of the interface converges exponentially fast to a stationary distribution and the interface moves with an asymptotic velocity v(h). The mobility is shown to exist and to satisfy the Einstein relation: , where β is the inverse temperature. Received: 16 April 2002 / Accepted: 3 July 2002 Published online: 22 November 2002 RID="*" ID="*" Work partially supported by the N.S.F. through grants DMS-0071766 and DMS-0074152.     

Efficient generation of blue light by frequency doubling of a Nd:YAG laser operating on 4 F 3/24 I 9/2 transitions

Efficient room-temperature operation of ⁴ F _3/2⁴ I _9/2 transitions in diode-end-pumped Nd:YAG lasers at 946 nm and 938.5 nm is reported. 7.0-W continuous-wave output power at 946 nm and 3.9 W at 938.5 nm have been obtained. An analytical model has been developed for the quasi-three-level laser including the influence of energy-transfer upconversion. Frequency doubling of these transitions in periodically poled KTP generated blue light at 473 nm and 469 nm. Both single-pass extra-cavity as well as intracavity schemes have been investigated. Received: 31 July 2002 / Published online: 5 February 2003 RID="*" ID="*"Corresponding author. Fax: +46-8/750-5430, E-mail: stefan.bjurshagen@acreo.se     

The Stability of Magnetic VorticesRID="*"ID="*"Research on this paper was supported by NSERC under grant N7901

We study the linearized stability of n-vortex (n∈ℤ) solutions of the magnetic Ginzburg–Landau (or Abelian Higgs) equations. We prove that the fundamental vortices (n = ± 1) are stable for all values of the coupling constant, λ, and we prove that the higher-degree vortices (|n|≥ 2) are stable for λ < 1, and unstable for λ > 1. This resolves a long-standing conjecture (see, eg, [JT]). Received: 16 November 1998 / Accepted: 3 January 2000 RID="*" ID="*"Research on this paper was supported by NSERC under grant N7901 RID="**" ID="**"Present address: Courant Institute, 251 Mercer St., New York, NY 10012, USA.&para;E-mail: gustaf&commat;cims.nyu.edu     

A Locally Compact Quantum Group Analogue of the Normalizer of SU(1,1) in SL(2, ℂ)

 S.L. Woronowicz proved in 1991 that quantum SU(1,1) does not exist as a locally compact quantum group. Results by L.I. Korogodsky in 1994 and more recently by Woronowicz gave strong indications that the normalizer of SU(1,1) in SL(2,ℂ) is a much better quantization candidate than SU(1,1) itself. In this paper we show that this is indeed the case by constructing , a new example of a unimodular locally compact quantum group (depending on a parameter 0<q<1) that is a deformation of . After defining the underlying von Neumann algebra of we use a certain class of q-hypergeometric functions and their orthogonality relations to construct the comultiplication. The coassociativity of this comultiplication is the hardest result to establish. We define the Haar weight and obtain simple formulas for the antipode and its polar decomposition. As a final result we produce the underlying C ^* -algebra of . The proofs of all these results depend on various properties of q-hypergeometric ₁ϕ₁ functions. Received: 28 June 2001 / Accepted: 25 July 2002 Published online: 10 December 2002 RID="*" ID="*" Post-doctoral researcher of the Fund for Scientific Research – Flanders (Belgium) (F.W.O.) Communicated by L. Takhtajan     

Silicon nanowires grown from Au-coated Si substrate

Amorphous Si nanowires were grown on an Au-coated Si substrate by heat treatment at 1000 °C under an H₂ atmosphere. The nanowires have a length of several tens of a micron and a diameter of 10–20 nm. The growth mechanism of the nanowires was investigated and explained with a solid–liquid–solid model. Received: 11 July 2002 / Accepted: 7 July 2002 / Published online: 4 December 2002 RID="*" ID="*"Corresponding author. Fax: +86/10-62751615, E-mail: yudp@pku.edu.cn     

Experimental investigation of non-linear selective reflection at the interface of Cs atomic vapor and quartz

We present an experimental study of non-linear selective reflection (SR) at a quartz–Cs-vapor interface in a V-type three-level scheme. The non-linear selective reflection at the Cs D₂ resonance line (⁶ S _1/2F=4→⁶ P _3/2) is monitored with and without pumping. The sub-Doppler reflection spectrum is observed and the effect of pumping on the signal of the selective reflection is investigated. The experimental result is in agreement with the theoretical calculation. Received: 16 April 2002 / Revised version: 12 June 2002 / Published online: 25 September 2002 RID="*" ID="*"Corresponding author. Fax: +86-351/701-1500, E-mail: zhaojm@sxu.edu.cn     

Stress investigations of thin amorphous Ge-Se-Ga films

Thin chalcogenide films from the systems (GeSe₄)_1-xGa_x and (GeSe₅)_1-xGa_x with gallium contents up to 20 at. % have been prepared by vacuum evaporation and their stress has been investigated by a cantilever technique. The addition of gallium to the Ge-Se matrix plays an important role in stress formation in the films: films without gallium possess negligible stress, while all gallium-containing films are under compressive stress. The increase of the gallium content leads to structural changes and an increase in the density, which results in higher stress values. For all films, stress reduction with time is observed due to spontaneous relaxation. Received: 2 October 2002 / Accepted: 22 November 2002 / Published online: 28 March 2003 RID="*" ID="*"Corresponding author. Fax: +49-561/8044-136, E-mail: popov@schottky.physik.uni-kassel.de     

A Stochastic Model Associated with Enskog Equation and Its Kinetic Limit

 We examine a system of particles in which the particles travel deterministically in between stochastic collisions. The collisions are elastic and occur with probability ɛ ^d when two particles are at a distance σ. When the number of particles N goes to infinity and Nɛ ^d goes to a nonzero constant, we show that the particle density converges to a solution of the Enskog Equation. Received: 29 January 2002 / Accepted: 30 July 2002 Published online: 14 November 2002 RID="*" ID="*" Research supported in part by NSF Grant DMS-0072666     

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.     

Dielectric breakdown of rubber materials by femtosecond irradiation

We report the reversible micro-structuring of a synthetic rubber polymer (cis1,4-polybutadiene (PB)) by femtosecond laser illumination. Visco-elastic relaxation of the optically damaged region was observed. The recovery time, typically 10²–10⁴ ms, can be varied by changing the irradiation pulse energy. Multi-shot-induced damage recovers on the much longer scale of 10¹–10² s. It was found that the doping of PB by 4 wt. % of pentazadiene ([4-NO₂]–phenyl–N=N–N(C₃H₇)–N=N–phenyl–[4-NO₂]) reduces the threshold of light-induced photo-modification by 20%. This is explained by photo-induced (homolytic) cleavage of the pentazadiene bonds and formation of gaseous N₂, which facilitates material failure at the irradiated spot. The recovery of optical transmission can be applied to optical memory, optical and micro-mechanical applications. The underlying mechanism of the phenomenon is discussed in terms of anelastic α- and β-relaxation (polymer backbone and chains/coils relaxation, respectively). Received: 11 October 2001 / Accepted: 9 July 2002 / Published online: 25 October 2002 RID="*" ID="*"Corresponding author. Fax: +81-88/656-7598, E-mail: misawa@eco.tokushima-u.ac.jp