arXiv subjects

Pierre Le Doussal

Publications and source records attributed to Pierre Le Doussal.

269 records · Page 15Linked to original sources

arXiv1997

Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-dimensional Random Environments

Sinai's model of diffusion in one-dimension with random local bias is studied by a real space renormalization group which yields asymptotically exact long time results. The distribution of the position of a particle and the probability of it not returning to the origin are obtained, as well as the two-time distribution which exhibits "aging" with $\frac{\ln t}{\ln t'}$ scaling and a singularity at $\ln t =\ln t'$. The effects of a small uniform force are also studied. Extension to motion of many domain walls yields non-equilibrium time dependent correlations for the 1D random field Ising model with Glauber dynamics and "persistence" exponents of 1D reaction-diffusion models with random forces.

cond-mat↗

arXiv1997

Glassy trapping of manifolds in nonpotential random flows

We study the dynamics of polymers and elastic manifolds in non potential static random flows. We find that barriers are generated from combined effects of elasticity, disorder and thermal fluctuations. This leads to glassy trapping even in pure barrier-free divergenceless flows $v {f \to 0}{\sim} f^ϕ$ ($ϕ> 1$). The physics is described by a new RG fixed point at finite temperature. We compute the anomalous roughness $R \sim L^ζ$ and dynamical $t\sim L^z$ exponents for directed and isotropic manifolds.

cond-mat↗

arXiv1997

Moving glass theory of driven lattices with disorder

We study periodic structures, such as vortex lattices, moving in a random potential. As predicted in [T. Giamarchi, P. Le Doussal Phys. Rev. Lett. 76 3408 (1996)] the periodicity in the direction transverse to motion leads to a new class of driven systems: the Moving Glasses. We analyse using several RG techniques the properties at T=0 and $T>0$: (i) decay of translational long range order (ii) particles flow along static channels (iii) the channel pattern is highly correlated (iv) barriers to transverse motion. We demonstrate the existence of the ``transverse critical force'' at T=0. A ``static random force'' is shown to be generated by motion. Displacements grow logarithmically in $d=3$ and algebraically in $d=2$. The persistence of quasi long range translational order in $d=3$ at weak disorder, or large velocity leads to predict a topologically ordered ``Moving Bragg Glass''. This state continues the static Bragg glass and is stable at $T>0$, with non linear transverse response and linear asymptotic behavior. In $d=2$, or in $d=3$ at intermediate disorder, another moving glass exist (the Moving Transverse Glass) with smectic quasi order in the transverse direction. A phase diagram in $T$ force and disorder for static and moving structures is proposed. For correlated disorder we predict a ``moving Bose glass'' state with anisotropic transverse Meissner effect and transverse pinning. We discuss experimental consequences such as anomalous Hall effect in Wigner crystal and transverse critical current in vortex lattice.

cond-mat↗

arXiv1997

Aging and diffusion in low dimensional environments

We study out of equilibrium dynamics and aging for a particle diffusing in one dimensional environments, such as the random force Sinai model, as a toy model for low dimensional systems. We study fluctuations of two times $(t_w, t)$ quantities from the probability distribution $Q(z,t,t_w)$ of the relative displacement $z = x(t) - x(t_w)$ in the limit of large waiting time $t_w \to \infty$ using numerical and analytical techniques. We find three generic large time regimes: (i) a quasi-equilibrium regime (finite $τ=t-t_w$) where $Q(z,τ)$ satisfies a general FDT equation (ii) an asymptotic diffusion regime for large time separation where $Q(z) dz \sim \bar{Q}[L(t)/L(t_w)] dz/L(t)$ (iii) an intermediate ``aging'' regime for intermediate time separation ($h(t)/h(t_w)$ finite), with $Q(z,t,t') = f(z,h(t)/h(t')) $. In the unbiased Sinai model we find numerical evidence for regime (i) and (ii), and for (iii) with $\bar{Q(z,t,t')} = Q_0(z) f(h(t)/h(t'))$ and $h(t) \sim \ln t$. Since $h(t) \sim L(t)$ in Sinai's model there is a singularity in the diffusion regime to allow for regime (iii). A directed model, related to the biased Sinai model is solved and shows (ii) and (iii) with strong non self-averaging properties. Similarities and differences with mean field results are discussed. A general approach using scaling of next highest encountered barriers is proposed to predict aging properties, $h(t)$ and $f(x)$ in landscapes with fast growing barriers. We introduce a new exactly solvable model, with barriers and wells, which shows clearly diffusion and aging regimes with a rich variety of functions $h(t)$.

cond-mat.stat-mech↗

arXiv1997

Statics and Dynamics of Disordered Elastic Systems

We examine here various aspects of the statics and dynamics of disordered elastic systems such as manifolds and periodic systems. Although these objects look very similar and indeed share some underlying physics, periodic systems constitute a class of their own with markedly different properties. We focus on such systems, review the methods allowing to treat them, emphasize the shift of viewpoint compared to the physics of manifolds and discuss their physics in detail. As for the statics, periodicity helps the system to retain a quasi-translational order and to be stable with respect to the proliferation of free topological defects such as dislocations. A disordered periodic system thus leads to a glass phase with Bragg peaks: the Bragg glass. On the other hand, for driven lattices, transverse periodicity allows the system to retain its glassy nature, leading to a moving glass phase. The existence of these two phases has important theoretical and experimental consequences, in particular for vortex physics in superconductors, the physical system which is mainly focused here.

cond-mat.dis-nn↗

arXiv1996

Dynamics of particles and manifolds in a quenched random force field

We study the dynamics of a directed manifold of internal dimension D in a d-dimensional random force field. We obtain an exact solution for $d \to \infty$ and a Hartree approximation for finite d. They yield a Flory-like roughness exponent $ζ$ and a non trivial anomalous diffusion exponent $ν$ continuously dependent on the ratio $g_{T}/g_{L}$ of divergence-free ($g_{T}$) to potential ($g_{L}$) disorder strength. For the particle (D=0) our results agree with previous order $ε^2$ RG calculations. The time-translational invariant dynamics for $g_{T} >0$ smoothly crosses over to the previously studied ultrametric aging solution in the potential case.

cond-mat.dis-nn↗

arXiv1996

Glass phase of two-dimensional triangular elastic lattices with disorder

We study two dimensional triangular elastic lattices in a background of point disorder, excluding dislocations (tethered network). Using both (replica symmetric) static and (equilibrium) dynamic renormalization group for the corresponding $N=2$ component model, we find a transition to a glass phase for $T < T_g$, described by a plane of perturbative fixed points. The growth of displacements is found to be asymptotically isotropic with $u_T^2 \sim u_L^2 \sim A_1 \ln^2 r$, with universal subdominant anisotropy $u_T^2 - u_L^2 \sim A_2 \ln r$. where $A_1$ and $A_2$ depend continuously on temperature and the Poisson ratio $σ$. We also obtain the continuously varying dynamical exponent $z$. For the Cardy-Ostlund $N=1$ model, a particular case of the above model, we point out a discrepancy in the value of $A_1$ with other published results in the litterature. We find that our result reconciles the order of magnitude of the RG predictions with the most recent numerical simulations.

cond-mat.dis-nn↗

arXiv1996

Reply to the Comment on `` Moving glass phase of driven lattices ''

It was shown in our Letter that the novel glassy property of the moving lattice (transverse critical force and pinned channels) originate {\it only} from the periodicity in the {\it transverse} direction, i.e the underlying smectic density modes of the structure. Thus, contrarily to the claim of the Comment, these properties should be robust to the details of the structure along the direction of motion, even in the presence of a random force (we have demonstrated the existence of a random force in both directions) or dislocations between layers.

cond-mat↗

arXiv1996

Glassy behaviour in disordered systems with non-relaxational dynamics

We show that a family of disordered systems with non-relaxational dynamics may exhibit ``glassy'' behavior at nonzero temperature, although such a behavior appears to be ruled out by a face-value application of mean-field theory. Nevertheless, the roots of this behavior can be understood within mean-field theory itself, properly interpreted. Finite systems belonging to this family have a dynamical regime with a self-similar pattern of alternating periods of fast motion and trapping.

cond-mat↗

arXiv1996

Moving glass phase of driven lattices

We study periodic lattices, such as vortex lattices, driven by an external force in a random pinning potential. We show that effects of static disorder persist even at large velocity. It results in a novel moving glass state with topological order analogous to the static Bragg glass. The lattice flows through well-defined, elastically coupled, {\it % static} channels. We predict barriers to transverse motion resulting in finite transverse critical current. Experimental tests of the theory are proposed.

cond-mat↗

arXiv1995

Columnar defects and vortex fluctuations in layered superconductors

We investigate fluctuations of Josephson-coupled pancake vortices in layered superconductors in the presence of columnar defects. We study the thermodynamics of a single pancake stack pinned by columnar defects and obtain the temperature dependence of localization length, pinning energy and critical current. We study the creep regime and compute the crossover current between line-like creep and pancake-like creep motion. We find that columnar defects effectively increase interlayer Josephson coupling by suppressing thermal fluctuations of pancakes. This leads to an upward shift in the decoupling line most pronounced around the matching field.

cond-mat↗

arXiv1995

Variational theory of elastic manifolds with correlated disorder and localization of interacting quantum particles

We apply the gaussian variational method (GVM) to study the equilibrium statistical mechanics of the two related systems: (i) classical elastic manifolds, such as flux lattices, in presence of columnar disorder correlated along the $τ$ direction (ii) interacting quantum particles in a static random potential. We find localization by disorder, the localized phase being described by a replica symmetry broken solution confined to the mode $ω=0$. For classical systems we compute the correlation function of relative displacements. In $d=2+1$, in the absence of dislocations, the GVM allows to describes the Bose glass phase. Along the columns the displacements saturate at a length $l_{\perp}$ indicating flux-line localization. Perpendicularly to the columns long range order is destroyed. We find divergent tilt modulus $c_{44}=\infty$ and a $x \sim τ^{1/2}$ scaling. Quantum systems are studied using the analytic continuation from imaginary to real time $τ\to i t$. We compute the conductivity and find that it behaves at small frequency as $σ(ω) \approx ω^2$ in all dimensions ($d < 4$) for which disorder is relevant. We compute the quantum localization length $ξ$. In $d=1$, where the model also describes interacting fermions in a static random potential, we find a delocalization transition and obtain analytically both the low and high frequency behavior of the conductivity for any value of the interaction. We show that the marginality condition appears as the condition to obtain the correct physical behavior. Agreement with renormalization group results is found whenever it can be compared.

cond-mat↗

arXiv1995

Large time off-equilibrium dynamics of a manifold in a random potential

We study the out of equilibrium dynamics of an elastic manifold in a random potential using mean-field theory. We find two asymptotic time regimes: (i) stationary dynamics, (ii) slow aging dynamics with violation of equilibrium theorems. We obtain an analytical solution valid for all large times with universal scalings of two-time quantities with space. A non-analytic scaling function crosses over to ultrametricity when the correlations become long-range. We propose procedures to test numerically or experimentally the extent to which this scenario holds for a given system.

cond-mat↗

arXiv1995

Creep in One Dimension and Phenomenological Theory of Glass Dynamics

The dynamics of a glass transition is discussed in terms of the motion of a particle in a one dimensional correlated random potential. An exact calculation of the velocity $V$ under an applied force $f$ demonstrates a variety of dynamic regimes depending on the range of correlations. In a gaussian potential with correlator $C(x) = x^γ$, we find a transition from ohmic behaviour ($γ<0$) to creep motion $V \sim \exp(- const/f^μ )$ ($0<γ<1$). This provides a generic picture of the glass transition in systems where long range correlations in the effective disorder develop due to elasticity such as elastic manifolds subject to quenched disorder and the vortex glass transition in superconductors.

cond-mat↗

arXiv1995

Large times off-equilibrium dynamics of a particle in a random potential

We study the off-equilibrium dynamics of a particle in a general $N$-dimensional random potential when $N \to \infty$. We demonstrate the existence of two asymptotic time regimes: {\it i.} stationary dynamics, {\it ii.} slow aging dynamics with violation of equilibrium theorems. We derive the equations obeyed by the slowly varying part of the two-times correlation and response functions and obtain an analytical solution of these equations. For short-range correlated potentials we find that: {\it i.} the scaling function is non analytic at similar times and this behaviour crosses over to ultrametricity when the correlations become long range, {\it ii.} aging dynamics persists in the limit of zero confining mass with universal features for widely separated times. We compare with the numerical solution to the dynamical equations and generalize the dynamical equations to finite $N$ by extending the variational method to the dynamics.

cond-mat↗

arXiv1993

Rotational Invariance and the Theory of Directed Polymer Nematics

The consequences of rotational invariance in a recent theory of fluctuations in dilute polymer nematics are explored. A correct rotationally invariant free energy insures that anomalous couplings are not generated in a one-loop renormalization group calculation.

cond-mat↗

arXiv1992

Self-Consistent Theory of Polymerized Membranes

We study $D$-dimensional polymerized membranes embedded in $d$ dimensions using a self-consistent screening approximation. It is exact for large $d$ to order $1/d$, for any $d$ to order $ε=4-D$ and for $d=D$. For flat physical membranes ($D=2,d=3$) it predicts a roughness exponent $ζ=0.590$. For phantom membranes at the crumpling transition the size exponent is $ν=0.732$. It yields identical lower critical dimension for the flat phase and crumpling transition $D_{lc}(d)={2 d \over {d+1}}$ ($D_{lc}={\sqrt{2}}$ for codimension 1). For physical membranes with ${\it random}$ quenched curvature $ζ=0.775$ in the new $T=0$ flat phase in good agreement with simulations.

cond-mat↗