Analytic calculation of scaling dimensions: Tricritical hard squares and critical hard hexagons

The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance.     

Fiber-optic reflex sensor for in-line production measurement

The paper describes experiments concerning distance measurement with fiber-optic sensor and improvement of the measurement principle. The sensor probe was well-designed with a small structure and multi-function. The novel optical fiber probe arrangement as well as the possibilities of use for complex measurement problems are explained using the measurement of an internal screw thread as an example. The experimental results show that the measurement uncertainty of the thread minor diameter can reach ±10 μm, and the stability of the measurement system is better than 0.07%.     

Luttinger liquid with asymmetric dispersion

We present an extension of the Tomonaga-Luttinger model in which left and right-moving particles have different Fermi velocities. We derive expressions for one-particle Green's functions, momentum-distributions, density of states, charge compressibility and conductivity as functions of both the velocity difference ε and the strength of the interaction β. This allows us to identify a novel restricted region in the parameter space in which the system keeps the main features of a Luttinger liquid but with an unusual behavior of the density of states and the static charge compressibility κ. In particular κ diverges on the boundary of the restricted region, indicating the occurrence of a phase transition. Received 20 May 2002 / Received in final form 23 August 2002 Published online 19 November 2002     

Working group report: Quantum chromodynamics

This is the report of the subgroup QCD of Working Group-4 at WHEPP-9. We present the activities that had taken place in the subgroup and report some of the partial results arrived at following the discussion at the working group meetings.     

High power diode single-end-pumped Nd:YVO4 laser

A fiber-coupled diode-single-end-pumped Nd:YVO₄ laser with an Nd:YVO₄ crystal of 0.3 at% doping concentration and 3×3×10 mm³ dimensions was reported. 14.850 W of continuous-wave output power in an M² factor of 1.12 was obtained under pump power of 27.365 W, with an optical conversion efficiency of 60.49%, and a slope efficiency of 64.5%.     

ASYMPTOTIC BEHAVIOR OF THE DRIFT-DIFFUSION SEMICONDUCTOR EQUATIONS

This paper is devoted to the long time behavior for the Drift-diffusion semi-conductor equations. It is proved that the dynamical system has a compact, connected and maximal attractor when the mobilities are constants and generation-recombination term is the Auger model; as well as the semigroup S(t) defined by the solutions map is differential. Moreover the upper bound of Hausdorff dimension for the attractor is given.     

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

Maximum Principles for Infinite Dimensional Diffusion Equations

In this paper we prove the validity of the Maximum Principle for some class of elliptic and parabolic equations of diffusion type in infinite dimension. The main tools are Asplund’s theorem and Preiss’ theorem on differentiability of Lipschitz functions in Banach space.      

Backlund transformation and variable separation solutions for the generalized Nozhnik—Novikov—Veselov equation

Using the extended homogeneous balance method, the B?cklund transformation for a (2+1)-dimensional integrable model, the generalized Nizhnik－Novikov－Veselov (GNNV) equation, is first obtained. Also, making use of the B?cklund transformation, the GNNV equation is changed into three equations: linear, bilinear and trilinear form equations. Starting from these three equations, a rather general variable separation solution of the model is constructed. The abundant localized coherent structures of the model can be induced by the entrance of two variable-separated arbitrary functions.     

Physics with large extra dimensions

The recent understanding of string theory opens the possibility that the string scale can be as low as a few TeV. The apparent weakness of gravitational interactions can then be accounted by the existence of large internal dimensions, in the sub-millimeter region. Furthermore, our world must be confined to live on a brane transverse to these large dimensions, with which it interacts only gravitationally. In my lecture, I describe briefly this scenario which gives a new theoretical framework for solving the gauge hierarchy problem and the unification of all interactions. I also discuss a minimal embedding of the standard model, gauge coupling unification and proton stability. On leave from: Centre de Physique Théorique, Ecole Polytechnique, 91128 Palaiseau, Cedex, France.