Four-pion production in e^+e^- annihilation

Abstract. We calculate the processes and to in the low-energy expansion of the standard model. The chiral amplitudes of can be extended via resonance exchange to energies around 1 GeV. Higher-order effects have been included in the form of and double exchange and by performing a resummation of the pion form factor. The predicted cross sections and the branching ratios are in good agreement with the available data. Received: 8 March 2002 / Published online: 14 June 2002     

Fermion families and chirality through extra dimensions

We give a simple model to explain the origin of fermion families and chirality through the use of a domain wall-anti-domain wall pair placed in a five dimensional space-time. Received: 14 March 2002 / Revised version: 3 July 2002 / Published online: 27 September 2002 RID="a" ID="a" e-mail: erdem@likya.iyte.edu.tr     

Ultrametricity between states at different temperatures in spin-glasses

We prove the existence of correlations between the equilibrium states at different temperatures of the multi-p-spin spherical spin-glass models with continuous replica symmetry breaking: there is no chaos in temperature in these models. Furthermore, the overlaps satisfy ultrametric relations. As a consequence the Parisi tree is essentially the same at all temperatures with lower branches developing when lowering the temperature. We conjecture that the reference free energies of the clusters are also fixed at all temperatures as in the generalized random-energy model. Received 18 March 2002 / Received in final form 14 June 2002 Published online 1st October 2002 RID="a" ID="a"e-mail: tommaso.rizzo@inwind.it     

The odderon in high energy elastic pp scattering

We study the odderon contribution to elastic pp and scattering at high energies. Different models for the odderon–proton coupling are considered and their effects on the differential cross section in the dip region are investigated. We use a Regge fit by Donnachie and Landshoff as a framework and replace its odderon contribution by the different models. We consider two models for the odderon–proton impact factor proposed by Fukugita and Kwieciński and by Levin and Ryskin. In addition we construct a geometric model of the proton which allows us to put limits on the size of a possible diquark cluster in the proton. All models are able to describe the data well. The two models for the impact factor require the strong coupling constant to be fixed rather precisely. In the geometric model a relatively small diquark size is required to describe the data. Received: 1 February 2002 / Published online: 14 June 2002     

Electromagnetic form factors of bound nucleons revisited

We investigate the possible modifications of the nucleons' electromagnetic form factors in the framework of a modified Skyrme model allowing for nucleon deformation and using realistic nuclear mass distributions. We show that such effects are small in light nuclei Received: 19 November 2002 / Accepted: 3 December 2002 / Published online: 18 March 2003 RID="a" ID="a"Address after January 1st, 2003: Helmholtz Institut für Strahlen- und Kernphysik (Theorie), Universit?t Bonn, Nu?allee 14-16, D-53115 Bonn, Germany; e-mail: meissner@itkp.uni-bonn.de RID="b" ID="b"Present address: Helmholtz Institut für Strahlen- und Kernphysik (Theorie), Universit?t Bonn, D-53115 Bonn, Germany. Communicated by V. Vento     

Recent experimental data and the size of the quark in the constituent quark model

We use the constituent quark model (CQM) to describe CDF data on double parton cross section and HERA data on the ratio cross section of elastic and inelastic diffractive productions. Our estimate shows that the radius of the constituent quark turns out to be rather small, GeV^-2, in accordance with the assumption on which CQM is based. Received: 14 April 2002 / Published online: 9 August 2002     

Well-Posedness for the Linearized Motion of a Compressible Liquid with Free Surface Boundary

 We study the motion of a compressible perfect liquid body in vacuum. This can be through of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free surface. This leads to a free boundary problem for Euler's equations, where the regularity of the boundary enters to highest order. We prove linearized stability in Sobolev space assuming a ``physical condition', related to the fact that the pressure of a fluid has to be positive. Received: 23 September 2002 / Accepted: 2 December 2002 Published online: 14 April 2003 RID="⋆" ID="⋆" The author was supported in part by the National Science Foundation. Communicated by P. Constantin     

Supercurrent and local coupling in the Wess-Zumino model

We study the Wess-Zumino model with the coupling extended to a chiral superfield. In order to incorporate the renormalization effects a further external real field has to be introduced. It is then possible to derive a Callan-Symanzik equation and to prove renormalizability. By constructing the supercurrent in this context the whole machinery for describing the superconformal symmetries becomes available. The presence of the external fields allows also to define multiple insertions of all relevant composite operators. Interesting relations to the curved superspace treatment show up. Received: 12 April 2002 / Published online: 14 June 2002     

An Extension of the Beale-Kato-Majda Criterion for the Euler Equations

 The Beale-Kato-Majda criterion asserts that smooth solutions to the Euler equations remain bounded past T as long as is finite, ohgr; being the vorticity. We show how to replace this by a weaker statement, on , where Δ^j is a frequency localization around . Received: 27 February 2002 / Accepted: 29 July 2002 Published online: 14 November 2002     

Selective advantage of topological disorder in biological evolution

We examine a model of biological evolution of Eigen's quasispecies in a so-called holey fitness landscape, where the fitness of a site is either 0 (lethal site) or a uniform positive constant (viable site). The evolution dynamics is therefore determined by the topology of the genome space which is modelled by the random Bethe lattice. We use the effective medium and single-defect approximations to find the criteria under which the localized quasispecies cloud is created. We find that shorter genomes, which are more robust to random mutations than average, represent a selective advantage which we call “topological”. A way of assessing empirically the relative importance of reproductive success and topological advantage is suggested. Received 9 August 2002 / Received in final form 7 November 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: slanina@fzu.cz     

Sympathetic cooling rate of gas-phase ions in a radio-frequency-quadrupole ion trap

We theoretically investigated the mass dependence of the sympathetic cooling rate of gas-phase ions trapped in a linear radio-frequency-quadrupole ion trap. Using an a priori molecular dynamical calculation, tracing numerically with Newtonian equations of motion, we found that ions with a mass greater than 0.54±0.04 times that of the laser-cooled ions are sympathetically cooled; otherwise, they are heated. To understand the mass dependence obtained using the molecular-dynamical calculation, we made a heat-exchange model of sympathetic cooling, which shows that the factor of 0.54±0.04 is a consequence of absence of micro-motion along the axis of the linear ion trap. Received: 10 December 2001 / Revised version: 28 January 2002 / Published online: 14 March 2002     

Fluctuations of the quark densities in nuclei

We study the static scalar susceptibility of the nuclear medium, i.e., the change of the quark condensate for a small modification of the quark mass. In the linear sigma model it is linked to the in-medium sigma propagator and its magnitude increases due to the mixing with the softer modes of the nucleon-hole excitations. We show that the pseudoscalar susceptibility, which is large in the vacuum, owing to the smallness of the pion mass, follows the density evolution of the quark condensate and thus decreases. At normal nuclear matter density the two susceptibilities become much closer, a partial chiral symmetry restoration effect as they become equal when the full restoration is achieved. Received: 20 July 2002 / Accepted: 14 September 2002 / Published online: 21 January 2003 RID="a" ID="a"e-mail: chanfray@ipnl.in2p3.fr Communicated by A. Molinari     

Continuous-wave tunable Cr2+:ZnS laser

We report the first continuous-wave tunable over ∼280 nm around 2.3 μm room-temperature operation of a chemical vapor transport-grown and diffusion-doped Cr²⁺:ZnS laser, pumped by a Co:MgF₂ laser at 1.67 μm and generating over 100 mW of output power at 16% slope efficiency. The self-consistent results of the laser and spectroscopic analysis demonstrate a large potential of this crystal as an active medium for diode-pumped tunable mid-infrared sources. Received: 7 January 2002 / Revised: 14 March 2002 / Published online: 2 May 2002     

Exponential Mixing of the 2D Stochastic Navier-Stokes Dynamics

 We consider the Navier-Stokes equation on a two dimensional torus with a random force which is white noise in time, and excites only a finite number of modes. The number of excited modes depends on the viscosity ν, and grows like ν ^-3 when ν goes to zero. We prove that this Markov process has a unique invariant measure and is exponentially mixing in time. Received: 14 March 2002 / Accepted: 7 May 2002 Published online: 22 August 2002     

Growth of fractal patterns during irradiation-induced amorphization in nano-sized Ni–W multilayers

In the Ni–W system, a uniform amorphous Ni–W phase was obtained by ion irradiation of the nano-sized Ni–W multilayers at liquid-nitrogen temperature. Interestingly, before undergoing complete amorphization, fractal patterns were observed at a relatively low irradiation dose (3×10¹⁴ Xe⁺/cm²), and the patterns were characterized to consist of crystalline grains of Ni-enriched solid solution. The fractal dimension was measured to be about 1.68±0.05, which was very close to that expected by the cluster diffusion-limited aggregation model. Received: 30 January 2002 / Accepted: 2 February 2002 / Published online: 3 May 2002     

DMRG studies on interchain coupling model for quasi-one-dimensional organic magnet

We introduce a solid-on-solid growth process which evolves by random deposition of dimers, surface diffusion, and evaporation of monomers from the edges of plateaus. It is shown that the model exhibits a robust transition from a smooth to a rough phase. The roughening transition is driven by an absorbing phase transition at the bottom layer of the interface, which displays the same type of critical behavior as the pair contact process with diffusion 2A↦3A, 2A↦. Received 14 October 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: Haye.Hinrichsen@physik.uni-wuppertal.de     

SQUID ratchets: basics and experiments

Superconducting quantum interference devices (SQUIDs) are very well suited for experimental investigations of ratchet effects. This is due to the periodicity of the Josephson coupling energy with respect to the phase difference δ of the superconducting macroscopic wave function across a Josephson junction. We show first that, within the resistively and capacitively shunted junction model, the equation of motion for δ is equivalent to the motion of a particle in the so-called tilted washboard potential, and we derive the conditions which have to be satisfied to build a ratchet potential based on asymmetric dc SQUIDs. We then present results from numerical simulations and experimental investigations of dc SQUID ratchets with critical-current asymmetry under harmonic excitation (periodically rocking ratchets). We discuss the impact of important properties like damping or thermal noise on the operation of SQUID ratchets in various regimes, such as adiabatically slow or fast nonadiabatic excitation. Received: 22 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Bispectral Operators of Prime Order

 The aim of this paper is to solve the bispectral problem for bispectral operators whose order is a prime number. More precisely we give a complete list of such bispectral operators. We use systematically the operator approach and in particular – Dixmier ideas on the first Weyl algebra. When the order is 2 the main theorem is exactly the result of Duistermaat-Grünbaum. On the other hand our proofs seem to be simpler. Received: 14 February 2002 / Accepted: 10 June 2002 Published online: 21 October 2002     

Intrinsic polarized strangeness and \Lambda ^0 polarization in deep-inelastic production

We propose a model for the longitudinal polarization of baryons produced in deep-inelastic lepton scattering at any , based on static SU(6) quark-diquark wave functions and polarized intrinsic strangeness in the nucleon associated with individual valence quarks. The free parameters of the model are fixed by fitting NOMAD data on the longitudinal polarization of hyperons in neutrino collisions. Our model correctly reproduces the observed dependences of the polarization on the kinematic variables. Within the context of our model, the NOMAD data imply that the intrinsic strangeness associated with a valence quark has anticorrelated polarization. We also compare our model predictions with results from the HERMES and E665 experiments using charged leptons. Predictions of our model for the COMPASS experiment are also presented. Received: 25 May 2002 / Revised version: 8 June 2002 / Published online: 7 October 2002     

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