Energy Profile Fluctuations in Dissipative Nonequilibrium Stationary States

The exact large deviation function (ldf) for the fluctuations of the energy density field is computed for a chain of Ising (or more generally Potts) spins driven by a zero-temperature (dissipative) Glauber dynamics and sustained in a nontrivial stationary regime by an arbitrary energy injection mechanism at the boundary of the system. It is found that this ldf is independent of the dynamical details of the energy injection, and that the energy fluctuations, unlike conservative systems in a nonequilibrium state, are not spatially correlated in the stationary regime.This revised version was published online in March 2005 with corrections to the page numbers.     

One-Dimensional Lattice Dynamics of the Diffusion-Limited Reaction A+A→A+S: Transient Behavior

We use a Boolean cellular automaton model to describe the diffusion-limited dynamics of the irreversible reaction A+AA+S on a 1D lattice. We derive a set of equations for the dynamics of the empty interval probabilities from which explicit expressions for the particle concentration and the two-point correlation can be obtained. It is shown that the long-time dynamics is in agreement with the off-lattice solution. The early-time behavior, however, predicts a slower decay of the concentration.     

An optimised molecular model for ammonia

Based on molecular dynamics (MD) computer simulations we investigate the dynamic behaviour of a model complex fluid suspension consisting of large (A) particles (the ‘solute’) immersed in a bath of smaller ‘solvent’ (B) particles. The goal is to identify the effect of systematic simplifications (coarse-graining) of the solvent on typical microscopic time correlation functions characterizing the single-particle and collective dynamics of the solute. As a reference system we employ a binary Lennard–Jones mixture of spherical particles with significant differences in particle sizes (σ_A>σ_B) and masses (m _A>m _B). We then replace the original B particles step by step by a reduced number of larger and heavier particles such that the mass and volume fraction of B particles is kept constant. At each step of coarse-graining, the intermolecular interactions between A particles are chosen such that the static A–A structure of the reference system is preserved. Our MD results indicate that coarse-graining has a profound influence on both the single-particle dynamics as reflected by the self-diffusion constant and the collective dynamics represented by the distinct part of the van Hove time correlation function. The latter holds only at intermediate packing fractions, whereas the collective dynamics turns out to be essentially insensitive to coarse-graining at high packing fractions.     

Mutual Annihilation of Two Diffusing Particles in One- and Two-Dimensional Lattices

The probabilistic dynamics of a pair of particles which can mutually annihilate in the course of their random walk on a lattice is considered and analytically found for d=1 and d=2. In view of available recent experiments achieved on the femtosecond scale, emphasis is put on the necessity of a full continuous-time, discrete-space solution at all times. Quantities of physical interest are calculated at any time, including the total pair survival probability N(t) and the two-particle correlation function. As a by-product, the lattice version allows for a precise regularization of the continuous-space framework, which is ill-conditionned for d2; this being done, formal generalization to any real dimensionality can be straightforwardly performed.     

Clusters in an assembly of globally coupled bistable oscillators

We study the dynamics of an assembly of globally coupled bistable elements. We show that bistability of elements results in some new features of clustering in the assembly when there is global coupling. We provide conditions for the existence of stable amplitude-phase clusters and splay-phase states. Received 12 June 1998 and Received in final form 30 November 1998     

Semiclassical theory for many-body fermionic systems

We present a treatment of many-body fermionic systems that facilitates an expression of well-known quantities in a series expansion inħ. The ensuing semiclassical result contains, to a leading order of the response function, the classical time correlation function of the observable followed by the Weyl-Wigner series; on top of these terms are the periodic-orbit correction terms. The treatment given here starts from linear response assumption of the many-body theory and in its connection with semiclassical theory, it assumes that the one-body quantal system has a classically chaotic dynamics. Applications of the framework are also discussed.     

The Vlasov equation for Coulomb systems and the Husimi picture

We explore the validity of the Vlasov equation as a semi-classical approximation of time-dependent Hartree-Fock and time-dependent LDA theories. We discuss the h → 0 limit for the propagation of quantal wavefunctions in terms of classical densities. The h → 0 limit is studied formally by means of its Wigner and Husimi phase-space representations. We consider an application to the valence electron cloud of metal clusters and show a comparison between quantal and Vlasov dynamics in this case.     

Control of spatiotemporal chaos: A study with an autocatalytic reaction-diffusion system

The characterization of chaotic spatiotemporal dynamics has been studied for a representative nonlinear autocatalytic reaction mechanism coupled with diffusion. This has been carried out by an analysis of the Lyapunov spectrum in spatiallylocalised regions. The linear scaling relationships observed in the invariant measures as a function of thesub-system size have been utilized to assess the controllability, stability and synchronization properties of the chaotic dynamics. The dynamical synchronization properties of this high-dimensional system has been analyzed using suitable Lyapunov functionals. The possibility of controlling spatiotemporal chaos for relevant objectives using available noisy scalar time-series data with simultaneous self-adaptation of the control parameter(s) has also been discussed.     

Pseudogap effects on the c-axis charge dynamics in copper oxide materials

The c-axis charge dynamics of copper oxide materials in the underdoped and optimally doped regimes has been studied by considering the incoherent interlayer hopping. It is shown that the c-axis charge dynamics for the chain copper oxide materials is mainly governed by the scattering from the in-plane fluctuation, and the c-axis charge dynamics for the no-chain copper oxide materials is dominated by the scattering from the in-plane fluctuation incorporating with the interlayer disorder, which would be suppressed when the holon pseudogap opens at low temperatures and lower doping levels, leading to the crossovers to the semiconducting-like range in the c-axis resistivity and the temperature linear to the nonlinear range in the in-plane resistivity. Received 29 July 1999 and Received in final form 24 January 2000     

Amorphous silicon hexaboride: a first-principles study

We report for the first time the atomic structure, electronic structure and mechanical properties of amorphous silicon hexaboride (a-SiB₆) based on first-principles molecular dynamics simulation. The a-SiB₆ model is generated from the melt and predominantly consists of pentagonal pyramid-like configurations and B₁₂ icosahedral molecules, similar to what has been observed in most boron-rich materials. The mean coordination number of B and Si atoms are 5.47 and 4.55, respectively. The model shows a semiconducting behaviour with a theoretical bandgap energy of 0.3?eV. The conduction tail states are found to be highly localised and hence the n-type doping is suggested to be more difficult than the p-type doping for a-SiB₆. The bulk modulus and Vickers hardness of a-SiB₆ are estimated to be about 118 and 13–17?GPa, respectively.     

Effects of the quantization ambiguities on the Big Bounce dynamics

In this paper, we investigate dynamics of the modified loop quantum cosmology models using dynamical systems methods. Modifications considered come from the choice of the different field strength operator F̂ and result in different forms of the effective Hamiltonian. Such an ambiguity of the choice of this expression from some class of functions is allowed in the framework of loop quantization. Our main goal is to show how such modifications can influence the bouncing universe scenario in the loop quantum cosmology. In effective models considered we classify all evolutional paths for all admissible initial conditions. The dynamics is reduced to the form of a dynamical system of the Newtonian type on a two-dimensional phase plane. These models are equivalent dynamically to the FRW models with the decaying effective cosmological term parameterized by the canonical variable p (or by the scale factor a). We demonstrate that the evolutional scenario depends on the geometrical constant parameter Λ as well as the model parameter n. We find that for the positive cosmological constant there is a class of oscillating models without the initial and final singularities. The new phenomenon is the appearance of curvature singularities for the finite values of the scale factor, but we find that for the positive cosmological constant these singularities can be avoided. The values of the parameter n and the cosmological constant differentiate asymptotic states of the evolution. For the positive cosmological constant the evolution begins at the asymptotic state in the past represented by the de Sitter contracting (deS₋) spacetime or the static Einstein universe H = 0 or H =  − ∞ state and reaches the de Sitter expanding state (deS₊), the state H = 0 or H =  + ∞ state. In the case of the negative cosmological constant we obtain the past and future asymptotic states as the Einstein static universes.     

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     

Strong decay to equilibrium in one-dimensional random spin systems

We consider a spin system on a lattice with finite-range, possibly unbounded random interactions. We show that for such systems the Glauber dynamics cannot decay to equilibrium exponentially fast inL ₂ even at high temperatures. Additionally, for one-dimensional systems with unbounded random couplings we prove that with probability one the corresponding Glauber dynamics has a fast (subexponential) decay to equilibrium in the uniform norm, provided that the distribution of random couplings satisfies some exponential bound.     

Universal homoclinic bifurcations and chaos near double resonances

We study the dynamics near the intersection of a weaker and a stronger resonance inn-degree-of-freedom, nearly integrable Hamiltonian systems. For a truncated normal form we show the existence of (n–2)-dimensional hyperbolic invariant tori whose whiskers intersect inmultipulse homoclinic orbits with large splitting angles. The homoclinic obits are doubly asymptotic to solutions that diffuse across the weak resonance along the strong resonance. We derive a universalhomoclinic tree that describes the bifurcations of these orbits, which are shown to survive in the full normal form. We illustrate our results on a three-degree-of-freedom mechanical system.     

A Hamiltonian yielding damped motion in an homogeneous magnetic field: quantum treatment

In earlier work, a Hamiltonian describing the classical motion of a particle moving in two dimensions under the combined influence of a perpendicular magnetic field and of a damping force proportional to the particle velocity, was indicated. Here we derive the quantum propagator for the Hamiltonian in different representations, one corresponding to momentum space, the other to position, and the third to a natural choice of “velocity” variables. We call attention to the following noteworthy fact: the Hamiltonian contains three parameters which do not in any way influence the motion of the position of the particle. However, at the quantum level, the propagator, even in the position representation, depends in an intricate way on these classically irrelevant parameters. This creates considerable doubt as to the validity of such a quantization procedure, as the physical results predicted differ for various Hamiltonians, all of which describe the dissipative dynamics equally well.     

Monte Carlo studies of a driven lattice gas. I. Growth and asymmetry during phase segregation

We investigate the effects of an external field on the kinetics of phase segregation in systems with conservative diffusive dynamics. We find that, in contrast to the situation without a field, there are now qualitative differences between the results of microscopic simulations of a 2D lattice model with biased Kawasaki exchanges and those obtained from various modifications of the macroscopic Cahn-Hilliard equation (mCH). While both microscopic simulations and numerical solutions of MCH yield triangular domains, we find that in the former the triangles mainly pointopposite to the field, while in the latter and in new calculations with the mCH they pointalong the field. On the other hand, the rate of growth of the clusters and their final state, bands parallel to the field, are similar. This issue and the question of the mesoscopic behavior of cell dynamical systems is discussed but not resolved.     

Some characterizations of strange sets

A thermodynamic formalism is exhibited that is the canonical version of Halseyet al.'s microcanonical formulation. This formalism is applied to a four-scale Cantor set and it is shown that the singularity spectrum fails to uniquely encode the underlying dynamics.     

Dynamical dark energy models – dynamical system approach

We study the Friedmann-Robertson-Walker model with dynamical dark energy modelled in terms of the equation of state p _X = w _X (a(z)) ρ _X in which the coefficient w _X is parameterized by the scale factor a or redshift z. We use methods of qualitative analysis of differential equations to investigate the space of all admissible solutions for all initial conditions on the two-dimensional phase plane. We show advantages of representing this dynamics as a motion of a particle in the one-dimensional potential V(a). One of the features of this reduction is the possibility of investigating how typical big rip singularities are in the future evolution of the model. The properties of potential function V can serve as a tool for qualitative classification of all evolution paths. Some important features like resolution of the acceleration problem can be simply visualized as domains on the phase plane. Then one is able to see how large is the class of solutions (labelled by the inset of the initial conditions) leading to the desired property.     

p-adic dynamics

The quadratic map overp-adic numbers is studied in some detail. We prove that near almost all indifferent fixed points it is topologically conjugate to a quasiperiodic linear map. We also establish the existence of chaotic behavior and describe it using symbolic dynamics.     

Solitons in Josephson junctions: An overview

The dynamics of the Josephson tunnel junction is approximately described by a perturbed sine-Gordon equation. The Josephson tunnel junction is thus a convenient experimental solid state device for the study of solitons and solitonlike phenomena. The physical manifestation of the soliton is a propagating magnetic flux quantum ( ₀=h/2e=2.064×10^–15 V sec). Basic properties of the soliton and its relation to observable experimental quantities (zero field steps, microwave radiation, etc.) are reviewed. Recent direct measurements of the actual soliton profile are also mentioned.