Showing papers in "Journal De Physique I in 1994"

Off equilibrium dynamics and aging in unfrustrated systems

Abstract: We analyse the Langevin dynamics of the random walk, the scalar field, the X-Y model and the spinoidal decomposition. We study the deviations from the equilibrium dynamics theorems (FDT and homogeneity), the asymptotic behaviour of the systems and the aging phenomena. We compare the results with the dynamcal behaviour of (random) spin-glass mean-field models.

The Black-Scholes option pricing problem in mathematical finance : generalization and extensions for a large class of stochastic processes

Abstract: The ability to price risks and devise optimal investment strategies in the presence of an uncertain "random" market is the cornerstone of modern finance theory. We first consider the simplest such problem of a so-called "European call option" initially solved by Black and Scholes using Ito stochastic calculus for markets modelled by a log-Brownien stochastic process. A simple and powerful formalism is presented which allows us to generalize the analysis to a large class of stochastic processes, such as ARCH, jump or Levy processes. We also address the case of correlated Gaussian processes, which is shown to be a good description of three different market indices (MATIF, CAC40, FTSE100). Our main result is the introduction of the concept of an optimal strategy in the sense of (functional) minimization of the risk with respect to the portfolio. If the risk may be made to vanish for particular continuous uncorrelated 'quasiGaussian' stochastic processes (including Black and Scholes model), this is no longer the case for more general stochastic processes. The value of the residual risk is obtained and suggests the concept of risk-corrected option prices. In the presence of very large deviations such as in Levy processes, new criteria for rational fixing of the option prices are discussed. We also apply our method to other types of options, `Asian', `American', and discuss new possibilities (`doubledecker'...). The inclusion of transaction costs leads to the appearance of a natural characteristic trading time scale.

A model for the dynamics of sandpile surfaces

Abstract: We propose a new continuum description of the dynamics of sandpile surfaces, which recognizes the existence of two populations of grains: immobile and rolling. The rolling grains are carried down the slope with a constant drift velocity and have a certain dispersion constant. We introduce a simple bilinear approximation for the interconversion process, which represents both the random sticking of rolling grains (below the angle of repose), and the dislodgement of immobile grains by rolling ones (for greater slopes). We predict that the mean downhill motion of rolling grains causes surface features to move uphill; shocks can arise at large amplitudes

Self induced quenched disorder: a model for the glass transition

Abstract: We consider a simple spin system without disorder which exhibits a glassy regime. We show that this mortel can be well approximated by a system with quenched disorder which is studied with the standard methods developed in spin glasses. We propose that the glass transition is a point where quenched disorder is self induced; a scenario for which the 'cavity' method might be particularly well suited.

Rectified motion induced by ac forces in periodic structures

Abstract: A particle in a periodic potential can be set into macroscopic motion by an ac force of zero mean value if the potential is asymmetric in space or the ac force is asymmetric in time. We analyze features of the resulting complex behaviour at zero and low temperatures within the framework of a simple sawtooth potential. This allows us to suggest experiments promoting separation methods and analysis of motor protein assemblies.

Photonic tunneling times

Abstract: We report on resonant and non-resonant photonic tunneling experiments. Resonant tunneling of wave packets has revealed a light localization, whereas the non-resonant barrier tunneling has corresponded to a zero-time barrier crossing. For a frequency-limited signal the non-resonant tunneling transmission time yielded superluminal group velocities, whereas in the case of a resonant transition the velocities are much slower than c

On the flux distribution in a one dimensional disordered system

Abstract: We study some transport properties of a one dimensional disordered system of finite length N. In this system particles are subject to random forces resulting both from a thermal noise and fom a quenched random force F(x) which models the inhomogeneous medium. The latter is distributed as a white noise with a non-zero average bias. Imposing some fixed concentration of particles at the end points of the chain yields a steady current J(N) which depends on the environments {F(x)}. The problem of computing the probability distribution P(J) over the environments is addressed. Our approach is based on a path integral method and on a moment calculation. In the case onf the non zero bias our results generalize those obtained recently by Oshanin et al

Sweeping of an instability : an alternative to self-organized criticality to get powerlaws without parameter tuning

Abstract: We show that a notable fraction of numerical and experimental works claiming the observation of self-organized criticality (SOC) rely in fact on a different physical mechanism, which involves the slow sweeping of a control parameter towards a global instability. This slow sweeping (which does not apparently involve a parameter tuning) has been the cause for the confusion with the characteristic SOC situation presenting truly no parameter tuning and functioning persistently in a marginal stability condition due to the operation of a feedback mechanism that ensures a steady state in which the system is marginally stable against a disturbance. The observation of power law distributions of events, often believed to be the hallmark of SOC, can be traced back to the cumulative measurements of fluctuations diverging on the approach of the critical instability. For non-critical instabilities such as first-order transitions, the power law distribution exists on a limiting size range up to a maximum value which is an increasing function of the range of interaction. We discuss the relevance of these ideas on the onset of spinodal decomposition, off-threshold multifractality, an exactly soluble model of rupture, the Burridge-Knopoff model of earthquakes, foreshocks and acoustic emissions, impact ionization breakdown in semiconductors, the Barkhausen effect, charge density waves, pinned flux lattices, elastic string in random potentials and real sandpiles.

Statistical mechanics and visual signal processing

Abstract: Nous montrons comment employer le langage de la theorie statistique des champs pour poser et resoudre des problemes ou l'on doit estimer une caracteristique de l'environnement a l'aide de donnees provenant d'un ensemble de detecteurs. Dans ce formalisme, l'estimateur optimal peut etre ecrit comme la valeur moyenne d'un operateur, l'ensemble des donnees d'entree agissant comme un champ externe. Les problemes a faible rapport signal-bruit sont resolus par la theorie des perturbations. La methode du col est employee pour ceux a haut rapport signal-bruit. Ces idees sont illustrees en details sur un modele d'estimation visuelle du mouvement base sur un probleme resolu par la mouche

Long-range correlated percolation and flow and transport in heterogeneous porous media

Abstract: We introduce a percolation model with long-range correlations, and investigate its scaling properties. Using this model, we provide a theoretical explanation for experimental data for hydrodynamic dispersion in heterogeneous rock formations and aquifers that had remained unexplained for a long time.

Interfaces and louver critical dimension in a spin glass model

Abstract: In this paper we try to estimate the louver critical dimension for replica symmetry breaking in spin glasses through the calculation of the additional free-energy required to create a domain wall between two different phases. This mechanism alone would say that replica symmetry would be restored at the louver critical dimension Dc = 2.5.

Field and frequency dependent transport in the two-dimensional organic conductor α-(BEDT-TTF)2I3

Abstract: The title compound undergoes a metal-insulator phase transition of unknown origin at TMI = 135 K. We studied the electrodynamic response of Q-(BEDT-TTFhh in a wide range of frequency, covering microwave and millimeter wave frequencies as weIl as the optical spectral range, and found a frequency dependent conductivity up to 1000 cm- 1 in the low temperature phase. This is accompanied be a non-linear transport with a smooth onset at about 10 V fcm. Our X-ray studies show no indication of superstructure reflections and clearly rule out the formation of a charge density wave ground state. The lack of a temperature dependence in the millimeter wave conductivity between 20 K and 100 K makes hopping transport unlikely.

Growth roughness and instabilities due to the Schwoebel effect : a one-dimensional model

Abstract: A very simple, one-dimensional model (Zeno model) of crystal growth by molecular beam epitaxy is studied numerically. The essentiel feature of the Zeno model is that it takes into account the asymetry of the sticking coefficient of adatoms to steps (Schwoebel effect), i.e., the diffusing atoms stick preferably to the upper ledge. In contrast with other, more microscopic descriptions, the Zeno model takes the diffusion of adatoms into account through a deterministic diffusion equation, so that the computing time is greatly reduced and a systematic investigation of the effect of the different parameters is possible. Deep cracks form even for a weak Schwoebel effect, but they form after a time which is very long if the Schwoebel effect is very weak. In certain cases, the roughness increases proportionally to time, in agreement with experiments on silicon and with other calculations. In the absence of Schwoebel effect, surface defects are healed during growth

Towards an experimental determination of the number of metastable states in spin-glasses?

Abstract: We argue that the systematic deviation from perfect aging (which means that the relaxation function only depend on the ratio t/t w , where t w is the waiting time) observed in spin-glasses can be accounted for if the number of available me astable states is finite. A significant fraction of these metastable states will be visited after an «ergodic» time which we estimate from the experiments to be: 106 seconds. This corresponds to ≃10 12 -10 14 different metastable states per independent subsystem

Statistical properties of one-point Green functions in disordered systems and critical behavior near the Anderson transition

Abstract: We investigate the statistics of local Green functions G (E, x, x)= , in particular of the local density of states ρ∞Im G (E, x, x), with the Hamiltonian H describing the motion of a quantum particle in a d-dimensional disordered system. Corresponding distributions are related to a function which plays the role of an order parameter for the Anderson metal-insulator transition. When the system can be described by a nonlinear σ-model, the distribution is shown to possess a specific inversion symmetry. We present an analysis of the critical behavior near the mobility edge that follows from the abovementioned relations. We explain the origin of the non-power-like critical behavior obtained earlier for effectively infinite-dimensional models. For any finite dimension d<∞ the critical behavior is demonstrated to be of the conventional power-law type with d=∞ playing the role of an upper critical dimension

Anisotropic effective medium theories

Abstract: The optical properties of anisotropic inhomogeneous media are studied within the framework of the classical 3D effective medium theories of Maxwell Garnett and Bruggeman, and the 2D theory of Yamaguchi et at. The origin of the anisotropy is either the nonspherical shape of the metallic inclusions in the 3D systems, or the distribution of the inclusions (even if spherical) on a substrate in the 2D configuration. In both cases, it leads to an anisotropic effective medium. In this paper, it is shown that this surrounding anisotropic medium induces a fictitious deformation of the inclusions which reduces the anisotropy and shifts the resonance wavelengths toward the sphere plasmon resonance. In the case of the mean field theory of Bruggeman, it also affects the percolation threshold value. Although some of these theories are now quite old, they are still extensively used, especially for the predictions of the absorption of the composite media. Therefore the effect presented here for the first time should be taken into account

Superconductivity and magnetic field induced spin density waves in the (TMTTF)2X family

Abstract: We report magnetotransport measurements in the quasi one dimensional (Q-1-D) organic conductor (TMTTF) 2 Br at pressures up to 26 kbar, down to 0.45 K in magnetic fields up to 19 T along the c * direction. It is found that a superconducting ground state is stabilized under 26 kbar at T c =0.8 K. No magnetic field induced spin density wave (FISDW) transitions are observed below 19T unlike other Q-1-D superconductors pertaining to the selenium series. The computed amplitude of the interchain coupling along transverse directions is unable to explain the missing FISDW instability

Recurrent clogging and density waves in granular material flowing through a narrow pipe

Abstract: We report on density waves in granular material, investigated both experimentally and numerically. When granular material falls through a long narrow pipe one observes recurrent clogging. The kinetic energy of the falling particles increases up to a characteristic threshold corresponding to the onset of recurrent clogging and density waves of no definite wavelength. The distances between regions of high density depend strongly on the initial conditions. They vary irregularly without any characteristic time and length scale. The particle-flow was investigated using 2D Molecular Dynamics simulations. Experimental investigations lead to equivalent results.

Low temperature dynamics of small γ-Fe203 particles

Abstract: We have studied the response of a system of small (∼4 nm) ferrimagnetic particles to a field reversal at low temperature (06 to 12 K) The reversal of the particle magnetic moments through the anisotropy barriers is shown to be governed by thermally activated dynamics down to 06 K, with no evidence for quantum effects We propose a data analysis in terms of the unique variable T-Ln(t/τ 0 ), which accounts for a non-constant distribution of anisotropy barriers

The first ET salt with a metal complex anion containing a selenocyanate ligand, (ET)2TIlHg(SeCN)4 : synthesis, structure and properties

Abstract: Synthesis of the first ET salt with a metal complex anion containing a selenocyanate ligand, α-(ET) 2 TlHg (SeCN) 4 , and its structure are reported. The temperature dependence of conductivity and thermopower in various crystallographic directions and the Shubnikov-de Haase oscillations have been studied. Distinctions of the bond length distributions in three crystallographically independent ET have been found, which may result in some charge localization in the radical-cation layer. A detailed comparison of the structure and properties of the compound obtained to its thiocyanate analog has been performed. It has been shown that in the α-(ET) 2 TlHg(SeCN) 4 salt there is no low-temperature phase transition characteristic of the α-(ET) 2 MHg(SCN) 4 compounds with M=K, Tl and Rb

Linear operators on correlated landscapes

Abstract: In this contribution we consider the effect of a class of «averaging operators» on isotropic fitness landscapes. Explicit expressions for the correlation function of the averaged landscapes are derived. A new class of tunably rugged landscapes, obtained by iterated smoothing of the random energy model, is established. The correlation structure of certain landscapes, among them the Sherrington-Kirkpatrick model, remains unchanged under the action of all averaging operators considered here

Rôle of dielectric effects in the red-green switching of porous silicon luminescence

Abstract: Trapping of a carrier at an ionized impurity in porous silicon may be significantly hindered when the material is embedded in a high-dielectric-constant medium such as an aqueous electrolyte. This effect is estimated for a geometry of cylindrical silicon wires, and by modeling the two media with wavevector-independent dielectric constants. The self-image potential of the electron is taken into account, and the frequency dependence of the outer dielectric constant is treated in a simple manner. The results demonstrate that the impurity states are not accessible in the presence of the electrolyte, just due to the dielectric relaxation of the embedding medium. This result may apply to different kinds of localized electronic states, including those responsible for the red luminescence in dry porous silicon. This provides a plausible explanation for the red to green switching of the luminescence when the porous silicon is wet and suggests that using embedding media of intermediate dielectric constants should allow one to observe a progressive transition Between red and green luminescence. Observation of porous silicon luminescence in solvents of various dielectric constants provides a preliminary test of this prediction

Depletion effect in a model lyotropic liquid crystal-theory

Abstract: The effect of added non-adsorbing polymer on the isotropic-nematic phase transition in a model lyotropic liquid crystal - a suspension of hard rods - is studied theoretically. The results indicate that the transition is widened and that polymer is partitioned preferentially into the more dilute isotropic phase. The concentration of polymer where a noticeable effect on the transition starts to occur is predicted to be of the order 5% of the coil overlap threshold c *

Interface roughening and pinning

Abstract: We study a simple model for the pinning of an interface by impurities with random strengths, and the depinning due to the applied pressure, in a quasi-static propagation limit. The model is very close to the so called «Robin Hood» model introduced by Zaitsev. It is designed to describe e.g. the invasion of a wetting fluid (imhibition) in a heterogeneous porous medium containing a second immiscible fluid. The relation between this model and other previously proposed approaches is discussed. The front of the invaded domain is shown to develop a self-affine structure with an increase of the roughness as a power-law of the injected volume. The value of the apparent roughness exponent can be favorably compared to some experimental measurements although we argue that the true roughness exponent is out of reach of commonly used methods. We show that the distribution f(d,Δt) of distances d between discrete local invasions at a time interval Δt can be described by a scaling law f(d,Δt) = d -1 φ(d/√Δt). This form can be obtained from the identification of a hierarchical structure of «bursts» in the pressure signal. Those «bursts» are qualitatively similar to those observed in quasistatic drainage, (i.e. invasion percolation), although characterized by different scaling indices

Solvable nineteen-vertex models and quantum spin chains of spin one

Abstract: We solved the Yang-Baxter equation for the R-matrices of three-state vertex models with ice condition, and obtained a complete list of solvable nineteen-vertex models and associated quantum spin Hamiltonians of spin one

Tunneling with dissipation

Abstract: Dissipative tunneling was studied with electromagnetic waves. Experiments were carried out with undersized waveguides loaded with a lossy dielectric medium which corresponds to a complex potential barrier. With increasing dissipation the Hartman effect disappears, i.e., the traversal time becomes dependent on barrier length. The results are in agreement with a recent phase time approach on complex tunneling

Experimental evidence of self organized criticality in the stick-slip dynamics of two rough elastic surfaces

Abstract: An expenment on the stick slip dynamics of two elastic rough surfaces is de- scnbed. This dynamics produces a self organized cntical state on a wide range of control parameters, namely loading speed and pressure. The dependence on the system size has also been studied. A comparison with the stick-slip dynamics produced by a one d1nlensional system and by two rigid surfaces is made.

A transfer matrix study of layering transitions in Ising model thin films

Abstract: We study the layering transitions for a spin 1/2 Ising model under uniform and variable magnetic field in a film of finite thickness limited by a single substrate. Using finite size transfer matrix and mean field theory, we show that the layering transitions occurs only at a temperature higher than T L . The latter depends on the nature of the surface field h s and on its strength H s . In the case where the surface field is short-range, the transfer matrix predicts a splitting of a single multi-layer transition into several single-layer transitions whereas mean field theory does not

The magnetic response of chaotic mesoscopic systems

Abstract: The magnetic response of mesoscopic systems with ballistic motion of electrons that is chaotic in the classical limit is considered. Semiclassical methods are applied in order to derive a formula for the susceptibility which is expressed in terms of a finite number of classical periodic orbits. This formula is used to study the fluctuations of the susceptibility in comparison with the fluctuations of random systems. Some of the mechanisms which lead to these fluctuations are discussed. At relatively high temperatures the formula for the susceptibility reduces to a simple expression in which only few short periodic orbits dominate the behavior. An experiment based on this result is proposed

CO2 and CO monolayers on MgO(100) : LEED experiments and potential energy calculations

Abstract: The structure of CO 2 and CO monolayers adsorbed on MgO(100) single crystal surfaces has been determined by both LEED and semi-empirical potential calculations. The CO 2 overlayer forms a commensurate (2√2×2√2)R45 o solid phase at T≤93±1 K. The CO monolayer forms a (4×2) commensurate phase at T≤40 K which is transformed into a (3×2) phase when 41 K≤T≤49 K. Above 50 K, the CO monolayer expands uniaxially toward a (n×2) phase with a progressive loss of long-range order when temperature increases. Potential calculations interpret very well the stable geometry for CO 2 and the sequential stability of the various commensurate phases for CO