Internal mode dynamics in driven nonlinear Klein-Gordon systems

We study analytically and numerically the action of a constant force on the propagation of kinks in the φ⁴ and sine-Gordon systems, with and without dissipation. We specifically investigate the relation of the external force with the oscillations of the kink width due to excitation of its internal mode or quasimode. We demonstrate that both dc force and dissipation, either jointly or separately, damp the oscillations of the kink width. We further prove that, in contrast to earlier predictions, those oscillations can only arise if we use a distorted kink as initial condition for the evolution. Finally, we show that for the φ⁴ system the oscillations of the kink width come from the excitation of its internal mode, whereas in the sG equation they originate in the excitation of the lowest radiational modes and an internal mode induced by the discreteness of the numerical simulations. Received 6 June 2000     

Weak localization and interaction in doped CdTe

We study weak localization and electron interaction in CdTe:In by low temperature magnetoconductance experiments to quantify the phase breaking length and the importance of interactions in CdTe. Then we study superconducting contacts to CdTe:In by transport measurements at very low temperature. The conductance-voltage characteristics of the superconducting contact exhibits the main features of a SIN junction, with a superimposed zero bias anomaly. This anomaly in the density of states of CdTe is very sensitive to magnetic field and probably induced by the proximity of the superconducting contact. Received 6 May 1998 and Received in final form 20 October 1998     

The temperature dependence of the perpendicular giant magnetoresistance in Co/Cu multilayered nanowires

A theory, based on earlier work by Valet and Fert, is first presented to describe the influence of temperature on the perpendicular giant magnetoresistance (GMR) in multilayers. Then we present GMR measurements performed at T=77 K and at room temperature on Co/Cu multilayered nanowires with layer thicknesses ranging from a few nm to 1 μm. We use our model to obtain a good quantitative fit to the experimental results in both the short spin diffusion length limit and out of this limit. We discuss the temperature dependence of the bulk parameters, the scattering spin asymmetry coefficient and spin diffusion length in the Co layers. Received: 25 January 1998 / Accepted: 6 May 1998     

Structure and size distribution of percolating clusters. Comparison with gelling systems

Dynamic properties of Brownian particles immersed in a periodic potential with two barriers V₁ and V₂ (symmetric bistable potential) are studied by using the Fokker-Planck equation which we solve numerically by the matrix continued fraction method. This study will therefore serve to demonstrate the influence of this form of potential, which is of great interest for superionic conductors and for many other solid systems, on the diffusion process. Thus, we have calculated the full width at half maximum (FWHM) ) of the quasi-elastic line of the dynamic structure factor, for a large range of values of the wave-vectors q. Our results show clearly that, by varying the ratio of the barriers strictly between and 1, the Fokker-Planck equation describes a diffusive process which has some characteristic of jump and liquid-like regimes. While in the limit cases, i.e. when tends to or 1, the diffusion process can be described only by a simple jump motion. However, the jump-lengths corresponding to each limit case are not equal. In general the change of the ratio is found to have a significant effect on the character of the diffusive motion. We have also performed Fokker-Planck dynamics calculations of the diffusion coefficient in a bistable potential. We have found a good agreement between numerical calculations and analytical approximation results obtained in the high friction limit. Received 25 May 1998 and Received in final form 15 November 1998     

Inelastic relaxation and noise temperature in S/N/S junctions

We studied electronic relaxation in long diffusive superconductor/normal metal/superconductor (S/N/S) junctions by means of current noise and transport measurements down to very low temperature (100mK). Samples with normal metal lengths of 4, 10 and 60μm have been investigated. In all samples the shot noise increases very rapidly with the voltage. This is interpreted in terms of enhanced heating of the electron gas confined between the two S/N interfaces. Experimental results are analyzed quantitatively taking into account electron-phonon interaction and heat transfer through the S/N interfaces. Transport measurements reveal that in all samples the two S/N interfaces are connected incoherently, as shown by the reentrance of the resistance at low temperature. The complementarity of noise and transport measurements allows us to show that the energy dependence of the reentrance at low voltage is essentially due to the increasing effective temperature of the quasiparticles in the normal metal. Received 5 February 2002 / Received in final form 6 September 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: hoffmann@drfmc.ceng.cea.fr     

2D superconducting junction networks as detectors of radiation

Summary We present a careful study of the behaviour of the below-gap photoresponse in 2D arrays of superconducting junctions. We have included the effects of the temperature, not only through the white-noise current term, but also through theT-dependence of the junction coupling energy. In order to render our model more realistic we also consider the correction due to the self-field generated by the screening currents. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

Exact diffusion coefficient of self-gravitating Brownian particles in two dimensions

We derive the exact expression of the diffusion coefficient of a self-gravitating Brownian gas in two dimensions. Our formula generalizes the usual Einstein relation for a free Brownian motion to the context of two-dimensional gravity. We show the existence of a critical temperature T_c at which the diffusion coefficient vanishes. For T < T_c, the diffusion coefficient is negative and the gas undergoes gravitational collapse. This leads to the formation of a Dirac peak concentrating the whole mass in a finite time. We also stress that the critical temperature T_c is different from the collapse temperature T_* at which the partition function diverges. These quantities differ by a factor 1-1/N where N is the number of particles in the system. We provide clear evidence of this difference by explicitly solving the case N = 2. We also mention the analogy with the chemotactic aggregation of bacteria in biology, the formation of “atoms” in a two-dimensional (2D) plasma and the formation of dipoles or “supervortices” in 2D point vortex dynamics.     

Light scattering with swollen hexagonal phases

We investigate, using quasi-elastic light scattering, some features of the long-wavelength, low-frequency modes of the hexagonal phase often encountered in the study of lyotropic (surfactant-solvent) systems. The hexagonal phase is swollen by an oil-based ferrofluid, allowing magnetically aligned samples to be prepared. We show experimentally the anisotropy of the two lowest-frequency modes. We develop a model which predicts that these slow modes are associated to particle diffusion and tube motion. With the help of microscopic as well as phenomenological analyses, we suggest that the latter presumably corresponds to a peristaltic mode. Confinement effects on the one-dimensional, Brownian diffusion of the colloids along the tube axis together with the coupling between the two modes are studied experimentally, varying the tube diameter to particle size ratio. Received 7 July 1999     

Functional renormalization description of the roughening transition

We reconsider the problem of the static thermal roughening of an elastic manifold at the critical dimension d=2 in a periodic potential, using a perturbative Functional Renormalization Group approach. Our aim is to describe the effective potential seen by the manifold below the roughening temperature on large length scales. We obtain analytically a flow equation for the potential and surface tension of the manifold, valid for low temperatures. On a length scale L, the renormalized potential is made up of a succession of quasi parabolic wells, matching onto one another in a singular region of width for large L. For strong periodic potential, the perturbation theory breaks down, and we argue, based on a variational calculation, that the transition becomes first order. We also obtain numerically the step energy as a function of temperature, and relate our results to the existing experimental data on ⁴He. Finally, we examine the case of a non local elasticity which is realized physically for the contact line. Received 16 April 1999 and Received in final form 11 October 1999     

Proximity effect in Fe/Pb/Fe trilayers

We have studied superconducting and magnetic properties of sputtered Fe/Pb/Fe-trilayers. For a fixed Pb thickness and with changing Fe thickness, , a monotonic decrease of the superconducting transition temperature was observed. Magnetization measurements clearly showed that Fe remains ferromagnetic down to the monolayer range. A quantitative comparison of with the theory of pair breaking by the exchange field reveals that the observed -suppression by the ferromagnetic Fe-layer is much weaker than expected. Possible reasons for the reduced -suppression in this system are discussed. Received: 30 June 1997 / Revised: 20 August 1997 / Accepted: 16 December 1997     

Brownian particles far from equilibrium

We study a model of Brownian particles which are pumped with energy by means of a non-linear friction function, for which different types are discussed. A suitable expression for a non-linear, velocity-dependent friction function is derived by considering an internal energy depot of the Brownian particles. In this case, the friction function describes the pumping of energy in the range of small velocities, while in the range of large velocities the known limit of dissipative friction is reached. In order to investigate the influence of additional energy supply, we discuss the velocity distribution function for different cases. Analytical solutions of the corresponding Fokker-Planck equation in 2d are presented and compared with computer simulations. Different to the case of passive Brownian motion, we find several new features of the dynamics, such as the formation of limit cycles in the four-dimensional phase-space, a large mean squared displacement which increases quadratically with the energy supply, or non-equilibrium velocity distributions with crater-like form. Further, we point to some generalizations and possible applications of the model. Received 24 November 1999     

Adatom diffusion on a square lattice. Theoretical and numerical studies

A two-dimensional lattice-gas model with square symmetry is investigated by using the real-space renormalization group (RSRG) approach with blocks of different size and symmetries. It has been shown that the precision of the method depends strongly not only on the number of sites in the block but also on its symmetry. In general, the accuracy of the method increases with the number of sites in the block. The minimal relative error in determining the critical values of the interaction parameters is equal to . Using the RSRG method, we have explored phase diagrams of both a two-dimensional Ising spin model and of a square lattice gas with lateral interactions between adparticles. We also have investigated the influence of the attractive and repulsive interactions on both the thermodynamic properties of the lattice gas and the diffusion of adsorbed particles over surface. We have calculated adsorption isotherms and coverage dependences of the pair correlation function, isothermal susceptibility and the chemical diffusion coefficient. In addition, we have included in our analysis the interaction of the activated particle in the saddle point with its nearest neighbors. We have also used Monte Carlo (MC) technique to calculate these dependences. Despite the fact that both methods constitute very different approaches, the correspondence of the numerical data is surprisingly good. Therefore, we conclude that the RSRG approach can be applied to characterize the thermodynamic and kinetic properties of systems of particles with strong lateral interactions. Received 1st September 1998 and Received in final form 8 March 2000     

Simple stochastic models showing strong anomalous diffusion

We show that strong anomalous diffusion, i.e. where is a nonlinear function of q, is a generic phenomenon within a class of generalized continuous-time random walks. For such class of systems it is possible to compute analytically where n is an integer number. The presence of strong anomalous diffusion implies that the data collapse of the probability density function cannot hold, a part (sometimes) in the limit of very small , now . Moreover the comparison with previous numerical results shows that the shape of is not universal, i.e., one can have systems with the same but different F. Received 14 April 2000     

Block persistence

We define a block persistence probability p _l (t) as the probability that the order parameter integrated on a block of linear size l has never changed sign since the initial time in a phase-ordering process at finite temperature T<T _c . We argue that in the scaling limit of large blocks, where z is the growth exponent (), is the global (magnetization) persistence exponent and f(x) decays with the local (single spin) exponent for large x. This scaling is demonstrated at zero temperature for the diffusion equation and the large-n model, and generically it can be used to determine easily from simulations of coarsening models. We also argue that and the scaling function do not depend on temperature, leading to a definition of at finite temperature, whereas the local persistence probability decays exponentially due to thermal fluctuations. These ideas are applied to the study of persistence for conserved models. We illustrate our discussions by extensive numerical results. We also comment on the relation between this method and an alternative definition of at finite temperature recently introduced by Derrida [Phys. Rev. E 55, 3705 (1997)]. Received: 25 February 1998 / Revised: 24 July 1998 / Accepted: 27 July 1998     

Diffusion and electromigration on disordered surfaces

We study a one-dimensional disordered solid-on-solid model in which neighboring columns are shifted by quenched random phases. The static height-difference correlation function displays a minimum at a nonzero temperature. The model is equipped with volume-conserving surface diffusion dynamics, including a possible bias due to an electromigration force. In the case of Arrhenius jump rates a continuum equation for the evolution of macroscopic profiles is derived and confirmed by direct simulation. Dynamic surface fluctuations are investigated using simulations and phenomenological Langevin equations. In these equations the quenched disorder appears in the form of time-independent random forces. The disorder does not qualitatively change the roughening dynamics of near-equilibrium surfaces, but in the case of biased surface diffusion with Metropolis rates it induces a new roughening mechanism, which leads to an increase of the surface width as . Received 7 February 2000     

Dynamics of isolated twin boundary in (TMTSF)

Intermittent and irregular motion of isolated twin boundary (kink) in organic crystal (TMTSF)₂PF₆ was studied at room temperature. Both the local velocity and the time of intermission are determined not only by external stress and temperature but also by the time (t w) elapsed after the backward passage and before the following forward one. When the kink moves after longer t w, its velocity becomes smaller and the time of intermission longer. Both tend to saturate for t w longer than 10² s. This result indicates that some disorder is induced in the lattice by the backward motion and it is relaxed during t w. We also found that the effect of the backward motion of one kink on its following motion is equivalent quantitatively to that of the forward motion of the pair-created counterpart. Received: 14 April 1998 / Received in final form and Accepted: 1st September 1998     

Scaling behavior of a nonlinear oscillator with additive noise,white and colored

We study analytically and numerically the problem of a nonlinear mechanical oscillator with additive noise in the absence of damping. We show that the amplitude, the velocity and the energy of the oscillator grow algebraically with time. For Gaussian white noise, an analytical expression for the probability distribution function of the energy is obtained in the long-time limit. In the case of colored, Ornstein-Uhlenbeck noise, a self-consistent calculation leads to (different) anomalous diffusion exponents. Dimensional analysis yields the qualitative behavior of the prefactors (generalized diffusion constants) as a function of the correlation time. Received 10 October 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: mallick@spht.saclay.cea.fr     

Interfacial reaction kinetics

We study irreversible A-B reaction kinetics at a fixed interface separating two immiscible bulk phases, A and B. Coupled equations are derived for the hierarchy of many-body correlation functions. Postulating physically motivated bounds, closed equations result without the need for ad hoc decoupling approximations. We consider general dynamical exponent z, where is the rms diffusion distance after time t. At short times the number of reactions per unit area, , is 2nd order in the far-field reactant densities . For spatial dimensions dabove a critical value , simple mean field (MF) kinetics pertain, where Q_b is the local reactivity. For low dimensions , this MF regime is followed by 2nd order diffusion controlled (DC) kinetics, , provided . Logarithmic corrections arise in marginal cases. At long times, a cross-over to 1st order DC kinetics occurs: . A density depletion hole grows on the more dilute A side. In the symmetric case (), when the long time decay of the interfacial reactant density, , is determined by fluctuations in the initial reactant distribution, giving . Correspondingly, A-rich and B-rich regions develop at the interface analogously to the segregation effects established by other authors for the bulk reaction . For fluctuations are unimportant: local mean field theory applies at the interface (joint density distribution approximating the product of A and B densities) and . We apply our results to simple molecules (Fickian diffusion, z=2) and to several models of short-time polymer diffusion (z>2). Received 8 June 1998 and Received in final form 10 September 1999