Random Unitary Matrices, Permutations and Painlevé

This paper is concerned with certain connections between the ensemble of n×n unitary matrices – specifically the characteristic function of the random variable tr(U) – and combinatorics – specifically Ulam's problem concerning the distribution of the length of the longest increasing subsequence in permutation groups – and the appearance of Painlevé functions in the answers to apparently unrelated questions. Among the results is a representation in terms of a Painlevé V function for the characteristic function of tr(U) and (using recent results of Baik, Deift and Johansson) an expression in terms of a Painlevé II function for the limiting distribution of the length of the longest increasing subsequence in the hyperoctahedral groups. Received: 2 December 1998 / Accepted: 12 May 1999     

Phase Separation in Random Cluster Models III: Circuit Regularity

We study the droplet that results from conditioning the subcritical Fortuin-Kasteleyn random cluster model on the presence of an open circuit Γ encircling the origin and enclosing an area of at least (or exactly) n ². In this paper, we prove that the resulting circuit is highly regular: we define a notion of a regeneration site in such a way that, for any such site v∈Γ, the circuit Γ cuts through the radial line segment through v only at v. We show that, provided that the conditioned circuit is centred at the origin in a natural sense, the set of regeneration sites reaches into all parts of the circuit, with maximal distance from one such site to the next being at most logarithmic in n with high probability. The result provides a flexible control on the conditioned circuit that permits the use of surgical techniques to bound its fluctuations, and, as such, it plays a crucial role in the derivation of bounds on the local fluctuation of the circuit carried out in Hammond (, 2009; , 2009).     

SLE on Doubly-Connected Domains and the Winding of Loop-Erased Random Walks

Two-dimensional loop-erased random walks (LERWs) are random planar curves whose scaling limit is known to be a Schramm-Loewner evolution SLE _κ with parameter κ=2. In this note, some properties of an SLE _κ trace on doubly-connected domains are studied and a connection to passive scalar diffusion in a Burgers flow is emphasised. In particular, the endpoint probability distribution and winding probabilities for SLE₂ on a cylinder, starting from one boundary component and stopped when hitting the other, are found. A relation of the result to conditioned one-dimensional Brownian motion is pointed out. Moreover, this result permits to study the statistics of the winding number for SLE₂ with fixed endpoints. A solution for the endpoint distribution of SLE₄ on the cylinder is obtained and a relation to reflected Brownian motion pointed out.     

The Effect of Disorder on the Free-Energy for the Random Walk Pinning Model: Smoothing of the Phase Transition and Low Temperature Asymptotics

We consider the continuous time version of the Random Walk Pinning Model (RWPM), studied in (Berger and Toninelli (Electron. J. Probab., to appear) and Birkner and Sun (Ann. Inst. Henri Poincaré Probab. Stat. 46:414–441, 2010; ). Given a fixed realization of a random walk Y on ℤ ^d with jump rate ρ (that plays the role of the random medium), we modify the law of a random walk X on ℤ ^d with jump rate 1 by reweighting the paths, giving an energy reward proportional to the intersection time L_t(X,Y)=ò₀^t 1_Xs=Ys dsL_{t}(X,Y)=\int_{0}^{t} \mathbf {1}_{X_{s}=Y_{s}}\,\mathrm {d}s: the weight of the path under the new measure is exp (βL _t (X,Y)), β∈ℝ. As β increases, the system exhibits a delocalization/localization transition: there is a critical value β _c , such that if β>β _c the two walks stick together for almost-all Y realizations. A natural question is that of disorder relevance, that is whether the quenched and annealed systems have the same behavior. In this paper we investigate how the disorder modifies the shape of the free energy curve: (1) We prove that, in dimension d≥3, the presence of disorder makes the phase transition at least of second order. This, in dimension d≥4, contrasts with the fact that the phase transition of the annealed system is of first order. (2) In any dimension, we prove that disorder modifies the low temperature asymptotic of the free energy.     

Analytical Approach to the One-Dimensional Disordered Exclusion Process with Open Boundaries and Random Sequential Dynamics

A one-dimensional disordered particle hopping rate asymmetric exclusion process (ASEP) with open boundaries and a random sequential dynamics is studied analytically. Combining the exact results of the steady states in the pure case with a perturbative mean field-like approach the broken particle-hole symmetry is highlighted and the phase diagram is studied in the parameter space (α,β), where α and β represent respectively the injection rate and the extraction rate of particles. The model displays, as in the pure case, high-density, low-density and maximum-current phases. All critical lines are determined analytically showing that the high-density low-density first order phase transition occurs at α≠β. We show that the maximum-current phase extends its stability region as the disorder is increased and the usual -decay of the density profile in this phase is universal. Assuming that some exact results for the disordered model on a ring hold for a system with open boundaries, we derive some analytical results for platoon phase transition within the low-density phase and we give an analytical expression of its corresponding critical injection rate α ^*. As it was observed numerically (Bengrine et al. J. Phys. A: Math. Gen. 32:2527, [1999]), we show that the quenched disorder induces a cusp in the current-density relation at maximum flow in a certain region of parameter space and determine the analytical expression of its slope. The results of numerical simulations we develop agree with the analytical ones. Regular associate of ICTP.     

Nonequilibrium Thermodynamics of the First and Second Kind: Averages and Fluctuations

We elaborate and compare two approaches to nonequilibrium thermodynamics, the two-generator bracket formulation of time-evolution equations for averages and the macroscopic fluctuation theory, for a purely dissipative isothermal driven diffusive system under steady state conditions. The fluctuation dissipation relations of both approaches play an important role for a detailed comparison. The nonequilibrium Helmholtz free energies introduced in these two approaches differ as a result of boundary conditions. A Fokker-Planck equation derived by projection operator techniques properly reproduces long range fluctuations in nonequilibrium steady states and offers the most promising possibility to describe the physically relevant fluctuations around macroscopic averages for time-dependent nonequilibrium systems.     

The BABAR Database：Challenges,Trends and Projections

The BABAR database,based upon the Objectivity OO database management system,has been in production since early 1999,It has met its initial design requirements which were to accommodate a 100Hz event rate from the experiment at a scale of 200TB per year.However,with increased luminosity and changes in the physics requirements,these requirements have increased significantly for the current running period and will again increase in the future.New capabilities in the underlying ODBMS product,in particular those of multiple federation and read-only database support,have been incorporated into a new design that is backwards compatible with existing application code while offering scaling into the multi-petabyte size regime.Other optimizations,including the increased use of thghtly coupled CORBA servers and an improved awareness of space inefficiencies,are also playing a part in meeting the new scaling requirements.We discuss these optimizations and the prospects for further scaling enhancements to address the longer-term needs of the experiment.     

The non-commutative oscillator, symmetry and the Landau problem

The isotropic oscillator on a plane is discussed where the coordinate and momentum space are both considered to be non-commutative. We also discuss the symmetry properties of the oscillator for three separate cases when the non-commutative parameters Θ and for x and p-space, respectively, satisfy specific relations. We compare the Landau problem with the isotropic oscillator on non-commutative space and obtain a relation between the two non-commutative parameters and the magnetic field of the Landau problem.     

Diffraction and correlations at the LHC: definitions and observables

We note that the definition of diffractive events is a matter of convention. We discuss two possible “definitions”: one based on unitarity and the other on Large Rapidity Gaps (LRG) or Pomeron exchange. LRG can also arise from fluctuations and we quantify this effect and some of the related uncertainties. We find care must be taken in extracting the Pomeron contribution from LRG events. We show that long-range correlations in multiplicities can arise from the same multi-Pomeron diagrams that are responsible for LRG events, and we explain how early LHC data can illuminate our understanding of ‘soft’ interactions.     

Heavy-quark free energies,internal-energy and entropy contributions

We present lattice QCD results on heavy-quark free energies, extract from its temperature dependence the entropy and internal-energy contributions, and discuss the onset of medium effects that lead to screening of static quark–antiquark sources in a thermal medium. The detailed analysis of the temperature and distance dependence of the different contributions indicate the complex non-perturbative nature of strongly interacting matter. We shall discuss the necessity to include those effects in studies on the behavior of heavy quarks, heavy-quark bound states and their dissociation in the quark–gluon plasma phase.     

Nonlinear optical absorption and refraction in Ru, Pd, and Au nanoparticle suspensions

We present the results of studies of the nonlinear optical properties of Pd, Ru, and Au nanoparticles. We studied the nonlinear refraction and nonlinear absorption of suspensions of these nanoparticles at 1064-nm wavelength. A relatively strong nonlinear absorption of the Pd nanoparticles was observed in the case of 1064-nm, 50-ps pulses (β=2×10⁻⁹ m W⁻¹). The Ru and Pd nanoparticles showed weak negative nonlinear refraction (γ∼−(6–8)×10⁻¹⁶ m² W⁻¹) in this spectral range. In the case of the Au nanoparticles, a saturated absorption at 532 nm dominated over other nonlinear optical processes.     

Sooting turbulent jet flame: characterization and quantitative soot measurements

Computational fluid dynamics (CFD) modelers require high-quality experimental data sets for validation of their numerical tools. Preferred features for numerical simulations of a sooting, turbulent test case flame are simplicity (no pilot flame), well-defined boundary conditions, and sufficient soot production. This paper proposes a non-premixed C₂H₄/air turbulent jet flame to fill this role and presents an extensive database for soot model validation.     

Growth,spectral properties,and laser demonstration of Nd:GYSO crystal

A generic nonlocal nonlinear optical system with a diffusive type of nonlinearity is investigated analytically, using the homogeneous balance principle and the F-expansion technique. Exact traveling wave and soliton solutions are discovered. Numerical simulation of their propagation and interaction properties is carried out. Our results demonstrate that the nonlocal solitary waves can be manipulated and controlled by changing the nonlocality parameter.     

Remarks on Undecidability,Incompleteness and the Integrability Problem

In their seminal paper Undecidability and incompleteness in classical mechanics (Int. J. Theor. Phys. 30:1041–1073, 1991), N.C.A. da Costa and F.A. Doria introduced a powerful method for studying the appearance of undecidability and incompleteness in mathematics and theoretical physics. In this work their results are applied to integrability theory. Specifically, it is pointed out that it is not possible to expect the existence of an algorithm able to decide whether a given partial differential equation is integrable or not.     

Rare Events,Escape Rates and Quasistationarity: Some Exact Formulae

We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging from the metric theory of continuos fractions and the Shannon capacity of constrained systems to the decay rate of metastable states, are given. It is a pleasure to thank L. Bunimovich for calling our attention to formula (1.1) in the special case of the doubling map, and V. Baladi and M. Demers for discussions on this formula. We are indebted to the ESI where, during the Workshop on Hyperbolic Dynamical Systems with Singularities (2008), this work was started. L.C. thanks the ENS, Paris, where he was invited during part of this work. Also we like to thank the Institut Henri Poincare–Centre Emile Borel where, during the trimester Mécanique statistique, probabilités et systèmes de particules (2008), this work was finished. Finally, G.K. acknowledges the support by the DFG grant KE 514/7-1, and L.C. by the MIUR grant PRIN 2007B3RBEY.     

Absolute frequency measurements of wavelength standards 532 nm, 543 nm, 633 nm and 1540 nm

This paper describes the results of absolute frequency measurements of primary wavelength standards 633 nm, 543 nm, 532 nm, (iodine stabilized) and 1540 nm (acetylene stabilized) in CMI. The values obtained with Menlo Systems femtosecond frequency comb in CMI are compared with previous measurements of the same standards in BIPM, BEV and MPQ. Measured sub-Doppler linewidths and relative intensities of several hyperfine spectral components of iodine molecule are also presented.     

Possible anomalies in Higgs decay: charm-suppression and flavour-violation

It is suggested that the Higgs boson may have a branching ratio into the $c\bar{c}$ mode suppressed by several orders of magnitude compared with conventional predictions and in addition some small but detectable flavour-violating modes such as $b\bar{s}$ and $\tau \bar{\mu}$ . The suggestion is based on a scheme proposed and tested earlier for explaining the mixing pattern and mass hierarchy of fermions in terms of a rotating mass matrix. If confirmed, the effects would cast new light on the geometric origin of fermion generations and of the Higgs field itself.     

High-gain Al2O3:Nd3+ channel waveguide amplifiers at 880 nm, 1060 nm, and 1330 nm

Neodymium-doped aluminum oxide films with a range of Nd³⁺ concentrations are deposited on silicon wafers by reactive co-sputtering, and single-mode channel waveguides with various lengths are fabricated by reactive ion etching. Photoluminescence at 880, 1060, and 1330 nm from the Nd³⁺ ions with a lifetime of 325 μs is observed. Internal net gain at 845–945 nm, 1064, and 1330 nm is experimentally and theoretically investigated under continuous-wave excitation at 802 nm. Net optical gain of 6.3 dB/cm at 1064 nm and 1.93 dB/cm at 1330 nm is obtained in a 1.4-cm-long waveguide with a Nd³⁺ concentration of 1.68×10²⁰ cm^?3 when launching 45 mW of pump power. In longer waveguides a maximum gain of 14.4 dB and 5.1 dB is obtained at these wavelengths, respectively. Net optical gain is also observed in the range 865–930 nm and a peak gain of 1.57 dB/cm in a short and 3.0 dB in a 4.1-cm-long waveguide is obtained at 880 nm with a Nd³⁺ concentration of 0.65×10²⁰ cm^?3. By use of a rate-equation model, the gain on these three transitions is calculated, and the macroscopic parameter of energy-transfer upconversion as a function of Nd³⁺ concentration is derived. The high internal net gain indicates that Al₂O₃:Nd³⁺ channel waveguide amplifiers are suitable for providing gain in many integrated optical devices.