Off-center Li ions: solid state rotators described by Mathieu's nonlinear-oscillator equation

Substitutional impurity ions in crystals are known to displace off-center and to perform hindered rotations around the ideal lattice positions. The vibronic theory to describe both the off-center displacements and the hindered rotations by a single angular equation incorporates terms up to 3rd order in the off-center displacement coordinates. When the rotation is confined to a single plane, the corresponding vibronic equation is equivalent to Mathieu's equation. Extending our earlier work, we derive here the dipole-dipole coupling to take into account cooperative phenomena. We also derive the optical absorption band arising from dipolar transitions across “Mexican Hat” surfaces, and we show that hindered rotations gives rise to magnetic moments quantized in rotational bands. Received 18 October 2001 / Received in final form 5 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: allxrose@hotmail.com     

On planar fermions with quartic interaction at finite temperature and density

We study the breaking of parity symmetry in the 2+1 Gross-Neveu model at finite temperature with chemical potential μ, in the presence of an external magnetic field. We find that the requirement of gauge invariance, which is considered mandatory in the presence of gauge fields, breaks parity at any finite temperature and provides for dynamical mass generation, preventing symmetry restoration for any non-vanishing μ. The dynamical mass becomes negligibly small as temperature is raised. Received 4 April 2002 / Received in final form 12 July 2002 Published online 15 October 2002 RID="a" ID="a"e-mail: cabra@venus.fisica.unlp.edu.ar     

Relationships between a microscopic parameter and the stochastic equations for interface's evolution of two growth models

The relationship between a microscopic parameter p, that is related to the probability of choosing a mechanism of deposition, and the stochastic equation for the interface's evolution is studied for two different models. It is found that in one model, that is similar to ballistic deposition, the corresponding stochastic equation can be represented by a Kardar-Parisi-Zhang (KPZ) equation where both λ and ν depend on p in the following way: ν(p) = νp and λ(p) = λp ^3/2. Furthermore, in the other studied model, which is similar to random deposition with relaxation, the stochastic equation can be represented by an Edwards-Wilkinson (EW) equation where ν depends on p according to ν(p) = νp ². It is expected that these results will help to find a framework for the development of stochastic equations starting from microscopic details of growth models. Received 26 August 2002 / Received in final form 20 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: ealbano@inifta.unlp.edu.ar     

Genetic Algorithms as a tool in the study of aperiodic order,with application to the case of X-Ray diffraction spectra of GaAs-AlAs multilayer heterostructures

We present the first application of Genetic Algorithms to the analysis of data from an aperiodically ordered system, high resolution X-Ray diffraction spectra from multilayer heterostructures arranged according to a deterministic or random scheme. This method paves the way to the solution of the “inverse problem”, that is the retrieval of the generating disorder from the investigation of the spectra of an unknown sample having non crystallographic, non quasi-crystallographic order. Received 18 March 2002 / Received in final form 3 July 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: Evelyne.Lutton@inria.fr RID="b" ID="b"CNRS UMR 8502     

Hedgehog production in spatially correlated noise

The production of topological defects during a quench in a φ⁴ model is investigated. The influence of a spatially correlated noise on defect production in two and three dimensions is demonstrated. Received 28 August 2001 / Received in final form 11 February 2002 Published online 2 October 2002 RID="a" ID="a"Paper supported in part by ESF “COSLAB” Programme RID="b" ID="b"e-mail: sfdobrow@kinga.cyf-kr.edu.pl     

On N-wave type systems and their gauge equivalent

The class of nonlinear evolution equations (NLEE) - gauge equivalent to the N-wave equations related to the simple Lie algebra are derived and analyzed. They are written in terms of (x, t) ∈ satisfying r = rank nonlinear constraints. The corresponding Lax pairs and the time evolution of the scattering data are found. The Zakharov-Shabat dressing method is appropriately modified to construct their soliton solutions. Received 20 October 2001 / Received in final form 30 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg     

Quasi-periodic and periodic solutions for dynamical systems related to Korteweg-de Vries equation

We consider quasi-periodic and periodic (cnoidal) wave solutions of a set of n-component dynamical systems related to Korteweg-de Vries equation. Quasi-periodic wave solutions for these systems are expressed in terms of Novikov polynomials. Periodic solutions in terms of Hermite polynomials and generalized Hermite polynomials for dynamical systems related to Korteweg-de Vries equation are found. Received 15 October 2001 / Received in final form 6 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: nakostov@ie.bas.bg     

Shrinking  as a recipe for revealing classical-like properties of optical-potential cross-sections

A simple recipe for revealing classical-like properties of optical-potential cross-sections is proposed. The recipe is based on the fact that the classical properties are not expected to depend on the actual value of . This allows us to identify the classical-like characteristics of an optical-potential cross-section by simply repeating the calculation with different values of , and observing which properties of the cross-section are invariant. The method is applied to the cross-sections of a few optical potentials used to describe the recent data of light heavy-ion elastic scattering. An improved near-side/far-side decomposition is used to separate the near-side and far-side components of the optical-potential cross-sections. Received: 4 September 2001 / Accepted: 3 June 2002 / Published online: 26 November 2002 RID="a" ID="a"e-mail: anni@le.infn.it Communicated by V. Vento     

NMR study of the dissolution of laser-polarized xenon

NMR of laser-polarized xenon is used to probe the dissolution behaviour of the noble gas in different liquids. The dissolution and self-relaxation rates are extracted via a macroscopic model, and comparison of the decay rate of the xenon magnetization in deuterated and non-deuterated solvent pairs allows the determination of the pure dipole-dipole contribution to relaxation. A transient convective effect, tentatively assigned to the xenon concentration gradient, is observed and characterized by diffusion encoding MRI experiments. The flow of xenon penetrates inside the solvent near the walls of the NMR tube, the longitudinal images showing a “” shape, the transverse ones a “O” shape. This convection effect has implications for delivery conditions of laser-polarized xenon in continuous flow experiments and magnetic resonance imaging. Received 29 April 2002 / Received in final form 26 July 2002 Published online 22 October 2002 RID="a" ID="a"e-mail: hdesvaux@cea.fr RID="b" ID="b"URA CNRS/CEA 331     

The role of pinning and instability in a class of non-equilibrium growth models

We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model is considered for the purpose. Following standard coarse graining procedures, it is shown that in the large time, long distance limit, the continuum model predicts a curvature independent KPZ phase, thereby suppressing all explicit effects of curvature and local pinning in the system, in the “perturbative” limit. A direct numerical integration of this growth equation, in 1+1 dimensions, supports this observation below a critical parametric range, above which generic instabilities, in the form of isolated pillared structures lead to deviations from standard scaling behaviour. Possibilities of controlling this instability by introducing statistically “irrelevant" (in the sense of renormalisation groups) higher ordered nonlinearities have also been discussed. Received 23 April 2002 / Received in final form 24 July 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: akc@mpipks-dresden.mpg.de     

Measurement of 2+ 1 level lifetimes in 162Yb and 162Er by fast electronic scintillation timing

Lifetime measurements for the 2⁺ ₁ levels of ¹⁶²Er and ¹⁶²Yb were obtained in β⁺/ɛ decay at the Yale Moving Tape Collector by fast electronic scintillation timing of β⁺γ coincidences. Received: 2 September 2002 / Accepted: 1 October 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: mark.caprio@yale.edu Communicated by J. ?yst?     

Three-dimensional motion of a vortex filament and its relation to the localized induction hierarchy

Three-dimensional motion of a slender vortex tube, embedded in an inviscid incompressible fluid, is investigated under the localized induction approximation for the Euler equations. Using the method of matched asymptotic expansions in a small parameter ε, the ratio of core radius to curvature radius, the velocity of a vortex filament is derived to O(ε³), whereby the influence of elliptical deformation of the core due to the self-induced strain is taken into account. It is found that there is an integrable line in the core whose evolution obeys a summation of the first and third terms of the localized induction hierarchy. Received 2 October 2001 / Received in final form 10 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: yasuhide@math.kyushu-u.ac.jp     

Gamma-ray tracking: Utilizing new concepts in the detection of gamma-radiation

Gamma-ray tracking in a closed array of highly segmented HPGe detectors is a new concept for the detection of γ-radiation. Each of the interacting γ-rays is identified and separated by measuring the energies and positions of individual interactions and by applying tracking algorithms to reconstruct the scattering sequences, even if many γ-rays hit the array at the same time. The three-dimensional position and the energy of interactions are determined by using two-dimensionally segmented Ge detectors along with pulse-shape analysis of the signals. Such a detector will have new and much improved capabilities compared to current γ-ray spectrometer. One implementation of this concept, called GRETA (Gamma-Ray Energy Tracking Array), is currently being under development at LBNL. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: kvetter@lbl.gov     

Interaction of coupled higher order nonlinear Schrödinger equation solitons

The novel inelastic collision properties of two-soliton interaction for an n-component coupled higher order nonlinear Schr?dinger equation are studied. Some interesting features of three soliton interactions, related to the integrability of the n-component coupled higher order nonlinear Schr?dinger equation are also discussed. Received 17 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: abhijit@iitg.ernet.in RID="b" ID="b"e-mail: sasanka@iitg.ernet.in RID="c" ID="c"e-mail: sudipta@iitg.ernet.in     

Deviations from perfect memory in spin glass temperature cycling experiments

We study the deviations from perfect memory in negative temperature cycle spin glass experiments. It is known that the a.c. susceptibility after the temperature is raised back to its initial value is superimposed to the reference isothermal curve for large enough temperature jumps ΔT (perfect memory). For smaller ΔT, the deviation from this perfect memory has a striking non monotonous behavior: the `memory anomaly' is negative for small ΔT's, becomes positive for intermediate ΔT's, before vanishing for still larger ΔT's. We show that this interesting behavior can be reproduced by simple Random Energy trap models. We discuss an alternative interpretation in terms of droplets and temperature chaos. Received 23 May 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: sasaki@ipno.in2p3.fr     

New solutions of the shape equation

The general shape equation describing the forms of vesicles is a highly nonlinear partial differential equation for which only a few explicit solutions are known. These solvable cases are briefly reviewed and a new analytical solution which represents the class of the constant mean curvature surfaces is described. Pearling states of the tubular fluid membranes can be explained as a continuous deformation preserving membrane mean curvature. Received 2 February 2002 / Received in final form 4 February 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: mladenov@obzor.bio21.bas.bg     

Elastica hypoarealis

We examine the equilibria of a rigid loop in the plane, characterized by an energy functional quadratic in the curvature, subject to the constraints of fixed length and fixed enclosed area. Whereas the only non self-intersecting equilibrium corresponding to the fixed length constraint is the circle, the area constraint gives rise to distinct equilibria labeled by an integer. These configurations exhibit self-intersections and bifurcations as the area is reduced. In addition, not only can the Euler-Lagrange equation be integrated to provide a quadrature for the curvature but the embedding itself can be expressed as a local function of the curvature. Perturbations connecting equilibria are shown to satisfy a first order ODE which is readily solved. Analytical expressions for the energy as a function of the area are obtained in the limiting regimes. Received 18 October 2001 / Received in final form 31 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: capo@fis.cinvestav.mx RID="b" ID="b"e-mail: chryss@nuclecu.unam.mx RID="c" ID="c"e-mail: jemal@nuclecu.unam.mx     

Thermodynamics of rotating self-gravitating systems

We investigate the statistical equilibrium properties of a system of classical particles interacting via Newtonian gravity, enclosed in a three-dimensional spherical volume. Within a mean-field approximation, we derive an equation for the density profiles maximizing the microcanonical entropy and solve it numerically. At low angular momenta, i.e. for a slowly rotating system, the well-known gravitational collapse “transition” is recovered. At higher angular momenta, instead, rotational symmetry can spontaneously break down giving rise to more complex equilibrium configurations, such as double-clusters (“double stars”). We analyze the thermodynamics of the system and the stability of the different equilibrium configurations against rotational symmetry breaking, and provide the global phase diagram. Received 8 July 2002 Published online 15 October 2002 RID="a" ID="a"e-mail: demartino@hmi.de     

2H( 3He, t)2p reaction at 2 GeV

The exclusive ²H( ³He, t)2p reaction has been studied at 2 GeV for energy transfers up to 500 MeV and triton angles up to 3.4^°. The protons were measured in the large acceptance magnetic detector DIOGENE, in coincidence with the forward tritons detected in a dedicated magnetic arm. The energy transfer spectra extend well above the pion threshold. However, in the region of Δ excitation, the yield is less than 10% of the inclusive ²H( ³He, t) cross-section, which indicates the small contribution of the ΔN ↦ NN process. The angular distributions of the two protons in their center of mass have been analysed as a function of energy transfer and triton angle and a Legendre polynomial decomposition has been achieved. These data have been compared to a model based on a coupled-channel approach for describing the NN and NΔ systems. Received: 21 October 2002 / Accepted: 15 November 2002 / Published online: 11 March 2003 RID="a" ID="a"e-mail: ramstein@ipno.in2p3.fr RID="†" ID="†"Deceased. RID="†" ID="†"Deceased. RID="d" ID="d"Present adress: School of Engineering, J?nk?ping University, P.O. Box 1026, S-551 11 J?nk?ping, Sweden. Communicated by M. Gar?on     

Sensitivity of the pQCD deuteron structure to the nucleon form factors

We discuss the applicability of pQCD to the elastic scattering of electrons on protons and deuterons. We analyze the Q²-dependence of the reduced deuteron form factor, taking into account the recent data on the electric proton form factor and we find that the value of the QCD-scale parameter Λ differs essentially from the value Λ = 0.1 GeV, previously found using the dipole parametrization of the electromagnetic nucleon form factors G_E and G_M. Moreover, the predicted scaling behavior of the reduced deuteron form factor cannot be recovered in the Dirac and Pauli representations for the nucleon electromagnetic form factors. Received: 14 October 2002 / Accepted: 12 November 2002 / Published online: 11 March 2003 RID="a" ID="a"Permanent address: National Science Center KFTI, 310108 Kharkov, Ukraine. RID="b" ID="b"e-mail: etomasi@cea.fr Communicated by V.V. Anisovich