The leading Ruelle resonances of chaotic maps

The leading Ruelle resonances of typical chaotic maps, the perturbed cat map and the standard map, are calculated by variation. It is found that, excluding the resonance associated with the invariant density, the next subleading resonances are, approximately, the roots of the equation $z^4=\gamma$, where $\gamma$ is a positive number which characterizes the amount of stochasticity of the map. The results are verified by numerical computations, and the implications to the form factor of the corresponding quantum maps are discussed.Comment: 5 pages, 4 figures included. To appear in Phys. Rev.

Development of a tight-binding potential for bcc-Zr. Application to the study of vibrational properties

We present a tight-binding potential based on the moment expansion of the density of states, which includes up to the fifth moment. The potential is fitted to bcc and hcp Zr and it is applied to the computation of vibrational properties of bcc-Zr. In particular, we compute the isothermal elastic constants in the temperature range 1200K < T < 2000K by means of standard Monte Carlo simulation techniques. The agreement with experimental results is satisfactory, especially in the case of the stability of the lattice with respect to the shear associated with C'. However, the temperature decrease of the Cauchy pressure is not reproduced. The T=0K phonon frequencies of bcc-Zr are also computed. The potential predicts several instabilities of the bcc structure, and a crossing of the longitudinal and transverse modes in the (001) direction. This is in agreement with recent ab initio calculations in Sc, Ti, Hf, and La.Comment: 14 pages, 6 tables, 4 figures, revtex; the kinetic term of the isothermal elastic constants has been corrected (Eq. (4.1), Table VI and Figure 4

Hot scatterers and tracers for the transfer of heat in collisional dynamics

We introduce stochastic models for the transport of heat in systems described by local collisional dynamics. The dynamics consists of tracer particles moving through an array of hot scatterers describing the effect of heat baths at fixed temperatures. Those models have the structure of Markov renewal processes. We study their ergodic properties in details and provide a useful formula for the cumulant generating function of the time integrated energy current. We observe that out of thermal equilibrium, the generating function is not analytic. When the set of temperatures of the scatterers is fixed by the condition that in average no energy is exchanged between the scatterers and the system, different behaviours may arise. When the tracer particles are allowed to travel freely through the whole array of scatterers, the temperature profile is linear. If the particles are locked in between scatterers, the temperature profile becomes nonlinear. In both cases, the thermal conductivity is interpreted as a frequency of collision between tracers and scatterers

Role of chaos for the validity of statistical mechanics laws: diffusion and conduction

Several years after the pioneering work by Fermi Pasta and Ulam, fundamental questions about the link between dynamical and statistical properties remain still open in modern statistical mechanics. Particularly controversial is the role of deterministic chaos for the validity and consistency of statistical approaches. This contribution reexamines such a debated issue taking inspiration from the problem of diffusion and heat conduction in deterministic systems. Is microscopic chaos a necessary ingredient to observe such macroscopic phenomena?Comment: Latex, 27 pages, 10 eps-figures. Proceedings of the Conference "FPU 50 years since" Rome 7-8 May 200

The gravitational wave detector VIRGO

International audienc

The Virgo data acquisition system

International audienc

DENSITY OF D-STATES IN AMORPHOUS TRANSITION METAL ALLOYS

No abstract availabl

SPACE FILLING MODELS OF AMORPHOUS STRUCTURES

La structure des corps amorphes est déterminée par les liaisons chimiques entre les atomes et par les contraintes topologiques de remplissage de l'espace. Les amorphes métalliques présentent un ordre local icosaédrique incompatible avec la périodicité cristalline, mais qui peut exister dans des espaces tridimensionnels de courbure non nulle. D'où il a été suggéré de construire des modèles d'amorphes métalliques par pavage icosaédrique d'espace courbe qui sont ultérieurement décourbés en préservant au maximum l'ordre local. Différentes méthodes de décourbure utilisent les disinclinaisons (ou dislocations de rotation). A l'opposé, une autre méthode consiste à paver un espace, en moyenne euclidien, mais de courbure variant aléatoirement : les régions de courbure positive sont les centres de nucléation d'icosaèdres. Nous donnons des règles de somme sur les pavages qui relient la distribution du nombre de premiers voisins (définis par la construction de Voronoi) à la courbure de l'espace. Nous discutons aussi la structure des "quasi-cristaux" dans lesquels une symétrie d'ordre 5 (ou 10) est observée. Un ordre d'orientation est encore présent, mais l'ordre de translation a disparu. Ces "quasi-cristaux" sont à mettre en relation avec les structures non périodiques de R. Penrose, qui présentent un caractère self-similaire. Les structures des covalents tétraédriques amorphes et des éléments des groupes V et VI sont aussi envisagées.The structure of amorphous systems is determined by the chemical bond between atoms and the topological constraints of the space filling requirement. Amorphous metallic systems show an icosahedrical local order incompatible with crystalline periodicity, but such a local order may exist in 3 dimensional spaces with non vanishing curvature. Hence it has been suggested to build up models of amorphous metallic structure by tiling curved spaces with icosahedra : the structure is subsequently decurved by methods that preserve the local order. The concept of disclination (or rotation-dislocation) plays a central role in the decurving procedure. At the opposite, another method consists of tiling a randomly corrugated space which remains euclidean in the average : regions of positive curvature are the nucleation centers of icosahedral environments. We define sum rules that relate the distribution of coordination numbers (defined by the Voronoi construction) to the curvature of the space. We discuss also the structure of "quasi-crystals" in which a fivefold (or tenfold) symmetry has been observed. An orientational order is still present but the translational order has disappeared. These "quasi-crystals" have to be related to the non-periodic structures invented by R. Penrose : both show a self-similar character. Endly, the structures of covalent fourfold coordinated amorphous systems are discussed as well as the structure of group V and VI elements

GROWTH SEQUENCE OF Si-CLUSTERS : FROM A FEW ATOMS TO THE AMORPHOUS PHASE

We study the growth sequence of clusters of atoms bonded by s and p electronic interactions. It is demonstrated that, like in the case of central forces, the clusters bear little relation to the structures formed as subunits of tri or tetravalent crystalline lattices. The stability of the cluster increases with the number of bonds even if the bond formation is accompanied by bond angles substantially different from 109 or 120°. But, in contrast with the case of central forces, bond angles Si-Si-Si smaller than about 90° produce an increase in bond length accompanied by a weakening of the cluster cohesion. We find that in some case the system undergoes a Jahn-Teller distortion when the HOMO (Highest Occupied Molecular Orbital) is degenerate