Trapping aspects in enhanced diffusion

We study the superlinear diffusion x ²(t) t , > 1, in layered media containing random velocity fields. The superlinear behavior holds in the case of random velocities along thex direction accompanied by diffusional motion in the space transverse to it. The transverse space can be either Euclidean, fractal, or ultrametric. For a one-dimensional transverse space we derive exact expressions for the higher moments of the displacement. Furthermore, we investigate the propagatorP(x, t) along thex direction and establish its scaling behavior. Our analysis highlights the resemblance between the stretched-Gaussian behavior of the propagator and the stretched-exponential form of the survivial probability in the trapping problem; both show late crossover behavior.This work is dedicated to Prof. George H. Weiss.     

Influence of the Target Shape on the Transition Radiation from Relativistic Electrons

The problem of transition radiation from relativistic electrons in a translucent disc and a sphere is considered. It is shown that the shape and transverse dimensions of the target may significantly affect the spectral and angular characteristics of transition radiation in the frequency range ca ^–1 ( is the Lorentz factor of the electron and a is the characteristic transverse size of the target).     

The exact phase diagram of the quantumXY spin glass model in a transverse field

The infinite rangeXY spin glass model in a transverse field is investigated by means of the Trotter-Suzuki approach. The exact phase diagram is obtained showing that a spin glass transition takes place for non-zero values of the transverse field up to a critical value _c =1.440.01. The present numerically exact calculations are in good agreement with our previous approximate results and they clear remaining discrepancies from previous work.     

Global weak solutions and attractors of the three dimensional Maxwell-Bloch two level laser systems

The three-dimensional Maxwell-Bloch system governs the multi-longitudinal and transverse mode dynamics of two level wide aperture lasers in an optical ring cavity. The system is hyperbolic in the propagation direction, and dispersive in the transverse directions due to diffraction effects. A rich variety of optical patterns and chaos are present in the dynamics. We show the global existence of weak solutions inL ^p (2p<) spaces of the Maxwell-Bloch system under both absorbing and periodic boundary conditions. The weak solutions are unique within the class of solutions provided by our regularization procedure and approach a universal attractor which has only partial smoothing instead of theC smoothing property found in early works for the (longitudinal) one-dimensional and (transverse) two-dimensional cases. The idea of the proof makes essential use of both the hyperbolicity and dispersivity of the system. In the case of periodic boundary condition, our result depends on a conjectural Strichartz inequality.     

On the Weyl transverse frames in type I spacetimes

We apply a covariant and generic procedure to obtain explicit expressions of the transverse frames that a type I spacetime admits in terms of an arbitrary initial frame. We also present a simple and general algorithm to obtain the Weyl scalars ₂^T, ₀^T and ₄^T associated with these transverse frames. In both cases it is only necessary to choose a particular root of a cubic expression.     

Exact results for the dynamics of one-dimensional spin-systems

In this contribution we discuss the spin-dynamics of anisotropic one-dimensional spin 1/2X-Y-chains in a magnetic field. For special values of the parameters we solve the equation of motion for several spin-operators exactly. These results we use to calculate longitudinal and transverse dynamical correlation functions at temperatureT=, for an Ising chain in a transverse field also the first-order high-temperature correction is given.     

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. I. General Theory and Square-Lattice Chromatic Polynomial

We study the chromatic polynomials (= zero-temperature antiferromagnetic Potts-model partition functions) P _G (q) for m×n rectangular subsets of the square lattice, with m8 (free or periodic transverse boundary conditions) and n arbitrary (free longitudinal boundary conditions), using a transfer matrix in the Fortuin–Kasteleyn representation. In particular, we extract the limiting curves of partition-function zeros when n, which arise from the crossing in modulus of dominant eigenvalues (Beraha–Kahane–Weiss theorem). We also provide evidence that the Beraha numbers B ₂,B ₃,B ₄,B ₅ are limiting points of partition-function zeros as n whenever the strip width m is 7 (periodic transverse b.c.) or 8 (free transverse b.c.). Along the way, we prove that a noninteger Beraha number (except perhaps B ₁₀) cannot be a chromatic root of any graph.     

Forward $\pi^\circ$ production and associated transverse energy flow in deep-inelastic scattering at HERA

Deep-inelastic positron-proton interactions at low values of Bjorken-x down to which give rise to high transverse momentum -mesons are studied with the H1 experiment at HERA. The inclusive cross section for -mesons produced at small angles with respect to the proton remnant (the forward region) is presented as a function of the transverse momentum and energy of the and of the four-momentum transfer Q ² and Bjorken-x. Measurements are also presented of the transverse energy flow in events containing a forward -meson. Hadronic final state calculations based on QCD models implementing different parton evolution schemes are confronted with the data.Received: 8 April 2004, Revised: 7 July 2004, Published online: 30 July 2004Dedicated to the memory of Krzysztof Rybicki     

Energy and mass-number dependence of the dissociation temperature in hydrodynamical models

Transverse-momentum distributions of andK have been analyzed within a framework of the hydrodynamical model to obtain the dependence of the collective transverse flow and the dissociation temperatureT _d inpp- and -induced multiparticle production reactions. The main outcomes are the steadily increasing transverse flow and a slowly decreasingT _d as the incident energy increases. This behavior is in excellent agreement with early Landau's estimate. An extension of this to nucleus-nucleus collisions correctly gives account of the very soft component which has been observed in heavyion experiments.     

Production of neutral strange particles in muon-nucleon scattering at 490 GeV

The production ofK ⁰, and particles is studied in the E665 muon-nucleon experiment at Fermilab. The average multiplicities and squared transverse momenta are measured as a function ofx _F andW ². Most features of the data can be well described by the Lund model. Within this model, the data on the K⁰/^± ratios and on the averageK ⁰ multiplicity in the forward region favor a strangeness suppression factors/u in the fragmentation process near 0.20. Clear evidence for QCD effects is seen in the average squared transverse momentum ofK ⁰ and particles.Deceased     

Wave packet realization of lightlike states

We construct a new realization of lightlike particle states. The realization considered corresponds to objects which form partially localized wave packets in the space dimensions transverse to the direction of the lightlike momentum. The states of the transverse motion are classified by the representations of an algebraSU(1, 1) constructed of the generators of the conformal group. It is conjectured that this realization is suitable for the formulation of the parton-model of hadrons.Research supported in part by the U.S. Atomic Energy Commission under Contract No. AT(30-1)-4076.     

Local spin correlations in partially frustrated amorphous Fe-Mn

Mössbauer measurements in a-(Fe_0.765Mn_0.235)₇₈Sn₂Si₆B₁₄ have been performed with⁵⁷Fe and¹¹⁹Sn. Both hyperfine fields show a kink near 70 K, indicating a freezing of the transverse spins. The ratio of the two hyperfine fields contains information about the correlation of the transverse spins. The ratioB _hf(Sn)/B _hf(Fe) stays constant aboveT _xy and rises belowT _xy . This indicates an alignment of the transverse spins on a local scale, as was also found inAuFe and a-FeZr.     

On the nonergodicity of the transverse magnetization in the transverse Ising model

The nonergodic behavior exhibited by the transverse spin correlation function _q=0 ^xx (t) the transverse Ising model obtained as the solution of approximate kinetic equations (derived on the basis of Résibois and De Leener's method), is shown to be an intrinsic property of the model and not the result of the approximations made in the derivation of the kinetic equations.Chargé de Recherches au Fonds National Belge de la Recherche Scientifique.     

Angular dependence of Bose-Einstein correlations in interactions of π+ andK + mesons with protons and nuclei at 250 GeV/c

The angular dependence of Bose-Einstein correlations is studied in interactions of ⁺ andK ⁺ mesons with protons and nuclei at 250 GeV/c. The pion source is found to be elongated along the interaction axis in the c.m.s., with the ratioa between transverse and longitudinal dimension equal to 0.55±0.06 for the case of proton, 0.53±0.13 for the case ofAl and 0.33±0.21 for the case ofAu target. For meson-proton interactions, indication for an increase of the elongation is found with increasing event multiplicity, pair momentum and particle transverse momentum.Now at UIA, Wilrijk, Belgium     

The lifetime of the “ferroelectric” phonon in some perovskite crystals at low temperatures

The lifetime of a low-lying transverse optic phonon with the wave vectork=0 (ferroelectric phonon) in perovskite crystals having the Curie point at low temperatures is investigated. Using a phenomenological Hamiltonian it is shown that mainly the process, in which the ferroelectric phonon and the transverse acoustic phonon are destroyed in order to create another optic phonon from the same branch, determines the lifetime of a ferroelectric phonon. The general result is specialized for SrTiO₃, and the temperature dependence of, exhibiting anomalies in comparison with normal ionic crystals, is discussed.The author thanks Dr. M. Marvan of the Physical Faculty of Charles University in Prague and Dr. P. Glogar and Dr. M. Trlifaj of the Institute of Physics, Czechoslovak Academy of Sciences, in Prague for valuable remarks.     

Field theory of critical behavior in a driven diffusive system

We use a field theoretic renormalization group method to study the critical properties of a diffusive system with a single conserved density subject to a constant uniform external field. A fixed point stable belowd _c=5 is found to govern the critical behavior. Scaling forms of density correlation functions are derived and critical exponents are obtained to all orders in =5–d. Spatial correlations are found to be very anisotropic with elongated correlations along the external field. Long wavelength transverse fluctuations are suppressed completely to yield mean field transverse exponents.     

Pion-source geometry deduced from soft-pion interferometry in heavy-ion collisions at 650 A MeV

We report transverse,R _T , and longitudinal,R _L , source sizes extracted from two-pion interferometry analysis in the Au+Au and Nb + Nb interactions at 650 A MeV. For the Nb+Nb interactions, both,R _T andR _L , do not exceed the niobium nucleus radius. In the case of Au+Au collisions, the transverse size is larger than the longitudinal one being about 12 fm for the selection ofP ⁺ < 120=" mev/c.=" we=" also=" corroborate=" the=" existence=" of=" the=" previously=" reported=" specific=" three-pion=">One of us (T.S.) wishes to thank Professor M.I. Podgoretsky and Professor R.M. Weiner for interesting discussions and comments. We also wish to acknowledge remarks of Dr. B. Lörstad.     

Low temperature nonequilibrium dynamics in transverse Ising spin glass

The real part of the time-dependent ac susceptibility of the short-range Ising spin glass in a transverse field has been investigated at very low temperatures. We have used the quantum linear response theory and domain coarsening ideas of quantum droplet scaling theory. It is found that after a temperature quench to a temperature T ₁ (lower than the spin glass transition temperature T _g ) the ac susceptibility decreases with time approximately in a logarithmic way as the system tends to the equilibrium. It is shown that the transverse field of tunneling has unessential effect on the nonequilibrium dynamical properties of the magnetic droplet system. The role of quantum fluctuations in the behavior of the ac susceptibility is discussed.Received: 26 February 2004, Published online: 18 June 2004PACS: 75.40.Gb Dynamic properties (dynamic susceptibility, spin waves, spin diffusion, dynamic scaling, etc.) - 75.10.Nr Spin-glass and other random models - 75.50.Lk Spin glasses and other random magnets     

Single longitudinal and transverse mode operation of a hybrid unstable resonator TE CO2 laser

Single-mode operation of an atmospheric-pressure TE CO₂ laser is reported. Single longitudinal mode emission has been achieved by incorporating a low-pressure, transversely excited gain section in the same laser cavity as the atmospheric-pressure section. The effects of different resonator configurations on the system modal behaviour have been investigated and it is shown that unstable resonators are particularly suitable for controlling the transverse mode structure with a complete coverage of the excited medium. With an unstable resonator configuration, formed by a metallic convex mirror and a plane diffraction grating, single longitudinal and single transverse mode output pulses with energy up to 2 J have been produced on more than 40 lines of both the 9.4 m and 10.4 m bands. This technique can easily be scaled to larger aperture devices at higher extracted energies.