Birth and long-time stabilization of out-of-equilibrium coherent structures

We study an analytically tractable model with long-range interactions for which an out-of-equilibrium very long-lived coherent structure spontaneously appears. The dynamics of this model is indeed very peculiar: a bicluster forms at low energy and is stable for very long time, contrary to statistical mechanics predictions. We first explain the onset of the structure, by approximating the short time dynamics with a forced Burgers equation. The emergence of the bicluster is the signature of the shock waves present in the associated hydrodynamical equations. The striking quantitative agreement with the dynamics of the particles fully confirms this procedure. We then show that a very fast timescale can be singled out from a slower motion. This enables us to use an adiabatic approximation to derive an effective Hamiltonian that describes very well the long time dynamics. We then get an explanation of the very long time stability of the bicluster: this out-of-equilibrium state corresponds to a statistical equilibrium of an effective mean-field dynamics. Received 28 February 2002 / Received in final form 24 July 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: Thierry.Dauxois@ens-lyon.fr RID="b" ID="b"UMR-CNRS 5672 RID="c" ID="c"UMR 5582     

Strange attractor simulated on a quantum computer

We show that dissipative classical dynamics converging to a strange attractor can be simulated on a quantum computer. Such quantum computations allow to investigate efficiently the small scale structure of strange attractors, yielding new information inaccessible to classical computers. This opens new possibilities for quantum simulations of various dissipative processes in nature. Received 10 August 2002 Published online 29 October 2002 RID="a" ID="a"e-mail: dima@irsamc.ups-tlse.fr RID="b" ID="b"UMR 5626 du CNRS     

Metastable states of the Ising chain with Kawasaki dynamics

We consider a ferromagnetic Ising chain evolving under Kawasaki dynamics at zero temperature. We investigate the statistics of the blocking time, as well as various characteristics of the metastable configurations reached by the system, including the statistics of the final energy, the spin correlations, and the distribution of domain sizes. Results of extensive numerical simulations are compared with analytical predictions made for the a priori ensemble of all blocked configurations with equal weights. Qualitative differences are found, e.g. in the domain sizes, which are found to be neither statistically independent nor exponentially distributed. Received 24 October 2002 / Received in final form 13 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: luck@spht.saclay.cea.fr RID="b" ID="b"URA 2306 of CNRS     

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     

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     

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     

The modified nonlinear Schrödinger equation: facts and artefacts

We argue that the integrable modified nonlinear Schr?dinger equation with the nonlinearity dispersion term is the true starting point to analytically describe subpicosecond pulse dynamics in monomode fibers. Contrary to the known assertions, solitons of this equation are free of self-steepening and the breather formation is possible. Received 29 September 2001 / Received in final form 25 January 2002 Published online 2 October 2002 RID="a" ID="a"doktorov@dragon.bas-net.by     

Method of group foliation and non-invariant solutions of partial differential equations

Using the heavenly equation as an example, we propose the method of group foliation as a tool for obtaining non-invariant solutions of PDEs with infinite-dimensional symmetry groups. The method involves the study of compatibility of the given equations with a differential constraint, which is automorphic under a specific symmetry subgroup and therefore selects exactly one orbit of solutions. By studying the integrability conditions of this automorphic system, i.e. the resolving equations, one can provide an explicit foliation of the entire solution manifold into separate orbits. The new important feature of the method is the extensive use of the operators of invariant differentiation for the derivation of the resolving equations and for obtaining their particular solutions. Applying this method we obtain exact analytical solutions of the heavenly equation, non-invariant under any subgroup of the symmetry group of the equation. Received 13 September 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: sheftel@gursey.gov.tr     

On the finite size corrections to some random matching problems

We get back to the computation of the leading finite size corrections to some random link matching problems, first adressed by Mézard and Parisi [J. Phys. France 48, 1451 (1987)]. In the so-called bipartite case, their result is in contradiction with subsequent works. We show that they made some mistakes, and correcting them, we get the expected result. In the non bipartite case, we agree with their result but push the analytical treatment further. Received 28 April 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: giorgio.parisi@roma1.infn.it RID="b" ID="b"e-mail: matthieu.ratieville@roma1.infn.it     

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     

Chaotic dynamics in a storage-ring free electron laser

The temporal dynamics of a storage-ring Free Electron Laser is here investigated with particular attention to the case in which an external modulation is applied to the laser-electron beam detuning. The system is shown to produce bifurcations as well as chaotic regimes. The peculiarities of this phenomenon with respect to the analogous behaviour displayed by conventional laser sources are pointed out. Theoretical results, obtained by means of a phenomenological model reproducing the evolution of the main statistical parameters of the system, are shown to be in a good agreement with experiments carried out on the Super-ACO Free Electron Laser. Received 27 March 2002 / Received in final form 17 July 2002 Published online 21 January 2003 RID="a" ID="a"Present address: Sincrotone Trieste, 34012 Trieste, Italy. RID="b" ID="b"e-mail: fanelli@nada.kth.se     

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     

Study of the sound-vortex interaction: direct numerical simulations and experimental results

We present a study of sound propagation through a single vortex by direct numerical simulations (DNS) compared to experimental measurements. We analyse the amplitude and the phase shift of the sound wave when it interacts with the vortical flow and we display the focusing effects produced by the vortex. We show that the turbulent fluctuations have a little effect on the sound phase shift whereas they induce a strong defocusing effect on the sound amplitude. Received 9 October 2002 / Received in final form 20 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: rberthet@lps.ens.fr RID="b" ID="b"UMR CNRS 8550     

Optimized Monte Carlo analysis for generalized ensembles

We present a new, maximum-likelihood based method to combine data from a multiple number of Monte Carlo simulations performed within any type of ensemble. The method offers an efficient iterative scheme to obtain the density of states of a wide range of energies as well as of other macroscopic variables. It should in particular be useful for the study of systems with a rough energy landscape. Received 4 June 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: borg@alf.nbi.dk     

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     

Exciton-polariton solitary waves

Effects of the exciton and polariton dispersions and the nonlinear exciton and photon interactions on the properties of polariton solitons in molecular crystals are investigated. Higher-order terms and phase-modulation (chirp) are taken into account. Bright- and dark-soliton solutions of the resulting modified nonlinear Schr?dinger (NLS) equation are presented. Nonlinearity- and dispersion-induced critical points on the polariton dispersion curve are obtained, separating regions with different solutions. Received 2 October 2001 / Received in final form 23 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: Stoychev@issp.bas.bg     

Soliton dynamics in chiral molecular chains with first- and third-neighbour interactions

We investigate the propagation and interaction of solitons associated with circularly polarized vibrations in gyrotropic media. The chirality of the structure yields different dispersion laws and hence different phase and group velocities for the left- and right-handed modes. The helical arrangement of the monomers is modelled through first- and third-neighbour interactions. The dynamics of the excitations is governed by a system of coupled discrete nonlinear Schr?dinger equations which is studied both analytically and numerically. Depending on the initial conditions and the interaction constants, different evolutionary patterns are obtained corresponding to unbound or bound one- and two-soliton solutions. The results can be applied to the process of energy transfer in helical polymers. Received 1st October 2001 / Received in final form 30 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: krad@issp.bas.bg     

Statistical properties of eigenvalues for an operating quantum computer with static imperfections

We investigate the transition to quantum chaos, induced by static imperfections, for an operating quantum computer that simulates efficiently a dynamical quantum system, the sawtooth map. For the different dynamical regimes of the map, we discuss the quantum chaos border induced by static imperfections by analyzing the statistical properties of the quantum computer eigenvalues. For small imperfection strengths the level spacing statistics is close to the case of quasi-integrable systems while above the border it is described by the random matrix theory. We have found that the border drops exponentially with the number of qubits, both in the ergodic and quasi-integrable dynamical regimes of the map characterized by a complex phase space structure. On the contrary, the regime with integrable map dynamics remains more stable against static imperfections since in this case the border drops only algebraically with the number of qubits. Received 19 June 2002 / Received in final form 30 September 2002 Published online 17 Decembre 2002 RID="a" ID="a"e-mail: dima@irsamc.ups-tlse.fr RID="b" ID="b"UMR 5626 du CNRS     

Production of high quality shocks for equation of state experiments

In this paper we describe the quality requirements that a shock wave must fulfil to make equation of state (EOS) measurements possible: planarity, no-preheating and stationarity of the shock. Experimental measurements have been performed at the Max Planck Institut für Quantenoptik (Garching). We also present simple analytical models that allow to verify shock stationarity and absence of preheating. Received 17 June 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: batani@mib.infn.it RID="b" ID="b"Present address: Pro-beam, Behrinsta?e 6, 85152 Planegg b. München, Germany. RID="c" ID="c"UMR 7605     

On adiabatic N-soliton interactions and trace identities

We compare the Hamiltonian properties of the N-soliton solutions of the NLSE in the adiabatic approximation and show how it matches the Hamiltonian formulation for the complex Toda chain which describes the adiabatic N-soliton interactions. Received 21 October 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg