Results for "Pierre Le Doussal"

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Crossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatzJan 06 2014We show how our previous result based on the replica Bethe ansatz for the Kardar Parisi Zhang (KPZ) equation with the "half-flat" initial condition leads to the Airy$_2$ to Airy$_1$ (i.e. GUE to GOE) universal crossover one-point height distribution in ... More
Sinai model in presence of dilute absorbersJun 01 2009We study the Sinai model for the diffusion of a particle in a one dimension random potential in presence of a small concentration $\rho$ of perfect absorbers using the asymptotically exact real space renormalization method. We compute the survival probability, ... More
Maximum of an Airy process plus Brownian motion and memory in KPZ growthSep 19 2017We obtain several exact results for universal distributions involving the maximum of the Airy$_2$ process minus a parabola and plus a Brownian motion, with applications to the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality class. This allows ... More
Exact results and open questions in first principle functional RGSep 06 2008Some aspects of the functional RG (FRG) approach to pinned elastic manifolds (of internal dimension $d$) at finite temperature $T>0$ are reviewed and reexamined in this much expanded version of [Europhys. Lett. {\bf 76} 457 (2006)]. The particle limit ... More
Finite temperature Functional RG, droplets and decaying Burgers TurbulenceMay 19 2006The functional RG (FRG) approach to pinning of $d$-dimensional manifolds is reexamined at any temperature $T$. A simple relation between the coupling function $R(u)$ and a physical observable is shown in any $d$. In $d=0$ its beta function is displayed ... More
Chaos and residual correlations in pinned disordered systemsMay 27 2005Jun 08 2005We study, using functional renormalization (FRG), two copies of an elastic system pinned by mutually correlated random potentials. Short scale decorrelation depend on a non trivial boundary layer regime with (possibly multiple) chaos exponents. Large ... More
Interaction quench in a Lieb-Liniger model and the KPZ equation with flat initial conditionsFeb 06 2014Recent exact solutions of the 1D Kardar-Parisi-Zhang equation make use of the 1D integrable Lieb-Liniger model of interacting bosons. For flat initial conditions, it requires the knowledge of the overlap between the uniform state and arbitrary exact Bethe ... More
On integrable directed polymer models on the square latticeJun 16 2015Jan 02 2016In a recent work Povolotsky provided a three-parameter family of stochastic particle systems with zero-range interactions in one dimension which are integrable by coordinate Bethe ansatz. Using these results we obtain the corresponding condition for integrability ... More
Universality in the mean spatial shape of avalanchesJan 02 2016Jun 06 2016Quantifying the universality of avalanche observables beyond critical exponents is of current great interest in theory and experiments. Here, we improve the characterization of the spatio-temporal process inside avalanches in the universality class of ... More
SLE on doubly-connected domains and the winding of loop-erased random walksMar 22 2008Two-dimensional loop-erased random walks (LERWs) are random planar curves whose scaling limit is known to be a Schramm-Loewner evolution SLE_k with parameter k = 2. In this note, some properties of an SLE_k trace on doubly-connected domains are studied ... More
Glass transition of a particle in a random potential, front selection in nonlinear RG and entropic phenomena in Liouville and SinhGordon modelsMar 16 2000We study via RG, numerics, exact bounds and qualitative arguments the equilibrium Gibbs measure of a particle in a $d$-dimensional gaussian random potential with {\it translationally invariant logarithmic} spatial correlations. We show that for any $d ... More
Dislocations and Bragg glasses in two dimensionsOct 19 1998We discuss the question of the generation of topological defects (dislocations) by quenched disorder in two dimensional periodic systems. In a previous study [Phys. Rev. B {\bf 52} 1242 (1995)] we found that, contrarily to $d=3$, unpaired dislocations ... More
Self-Consistent Theory of Polymerized MembranesAug 27 1992We 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 $\epsilon=4-D$ and for $d=D$. For flat physical membranes ($D=2,d=3$) ... More
The Aharonov-Bohm effect in presence of dissipative environmentsJun 21 2010We study a particle on a ring in presence of various dissipative environments. We develop and solve a variational scheme assuming low frequency dominance. Our solution produces a renormalization group (RG) transformation to all orders in the inverse dissipation ... More
Interference in presence of DissipationFeb 16 2006Jun 06 2006We study a particle on a ring in presence of various dissipative environments. We develop and solve a variational scheme assuming low frequency dominance. We analyze our solution within a renormalization group (RG) scheme to all orders which reproduces ... More
Electromagnetic Coulomb Gas with Vector Charges and "Elastic'' Potentials : Renormalization Group EquationsJul 18 2007We present a detailed derivation of the renormalization group equations for two dimensional electromagnetic Coulomb gases whose charges lie on a triangular lattice (magnetic charges) and its dual (electric charges). The interactions between the charges ... More
Disordered XY models and Coulomb gases: renormalization via traveling wavesFeb 08 1998Feb 17 1998We present a novel RG approach to 2D random XY models using direct and replicated Coulomb gas methods. By including fusion of environments (charge fusion in the replicated CG) it follows the distribution of local disorder, found to obey a Kolmogorov non ... More
Melting of two dimensional solids on disordered substrateDec 18 1997We study 2D solids with weak substrate disorder, using Coulomb gas renormalisation. The melting transition is found to be replaced by a sharp crossover between a high $T$ liquid with thermally induced dislocations, and a low $T$ glassy regime with disorder ... More
Moving glass phase of driven latticesDec 01 1995Apr 25 1996We 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 ... More
Reply to the Comment on `` Moving glass phase of driven lattices ''Aug 29 1996It 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 ... More
Variational theory of elastic manifolds with correlated disorder and localization of interacting quantum particlesSep 02 1995We 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 $\tau$ direction (ii) ... More
Freezing transitions and the density of states of 2D random Dirac HamiltoniansAug 08 2001Using an exact mapping to disordered Coulomb gases, we introduce a novel method to study two dimensional Dirac fermions with quenched disorder in two dimensions which allows to treat non perturbative freezing phenomena. For purely random gauge disorder ... More
Localization of thermal packets and metastable states in Sinai modelFeb 18 2002We consider the Sinai model describing a particle diffusing in a 1D random force field. As shown by Golosov, this model exhibits a strong localization phenomenon for the thermal packet: the disorder average of the thermal distribution of the relative ... More
Joint min-max distribution and Edwards-Anderson's order parameter of the circular $1 / f$-noise modelApr 08 2016We calculate the joint min--max distribution and the Edwards-Anderson's order parameter for the circular model of $1 / f$-noise. Both quantities, as well as generalisations, are obtained exactly by combining the freezing-duality conjecture and Jack-polynomial ... More
Exact short-time height distribution in 1D KPZ equation with Brownian initial conditionMay 12 2017The early time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimension, starting from a Brownian initial condition with a drift $w$, is studied using the exact Fredholm determinant representation. For large drift we recover the exact results ... More
Moving glass theory of driven lattices with disorderAug 12 1997We 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: ... More
Disorder Induced Transitions in Layered Coulomb Gases and SuperconductorsFeb 02 2000A 3D layered system of charges with logarithmic interaction parallel to the layers and random dipoles is studied via a novel variational method and an energy rationale which reproduce the known phase diagram for a single layer. Increasing interlayer coupling ... More
Disordered free fermions and the Cardy Ostlund fixed line at low temperatureJul 25 2006Feb 12 2007Using functional RG, we reexamine the glass phase of the 2D random-field Sine Gordon model. It is described by a line of fixed points (FP) with a super-roughening amplitude $\bar{(u(0)-u(r))^2} \sim A(T) \ln^2 r $ as temperature $T$ is varied. A speculation ... More
Freezing of dynamical exponents in low dimensional random mediaJun 23 2000A particle in a random potential with logarithmic correlations in dimensions $d=1,2$ is shown to undergo a dynamical transition at $T_{dyn}>0$. In $d=1$ exact results demonstrate that $T_{dyn}=T_c$, the static glass transition temperature, and that the ... More
Large fluctuations of the KPZ equation in a half-spaceApr 24 2018Jul 26 2018We investigate the short-time regime of the KPZ equation in $1+1$ dimensions and develop a unifying method to obtain the height distribution in this regime, valid whenever an exact solution exists in the form of a Fredholm Pfaffian or determinant. These ... More
Log-Gamma directed polymer with fixed endpoints via the replica Bethe AnsatzJun 23 2014Nov 24 2014We study the model of a discrete directed polymer (DP) on the square lattice with homogeneous inverse gamma distribution of site random Boltzmann weights, introduced by Seppalainen. The integer moments of the partition sum, $\overline{Z^n}$, are studied ... More
Statistics of shocks in a toy model with heavy tailsDec 29 2013We study the energy minimization for a particle in a quadratic well in presence of short-ranged heavy-tailed disorder, as a toy model for an elastic manifold. The discrete model is shown to be described in the scaling limit by a continuum Poisson process ... More
Directed polymer near a hard wall and KPZ equation in the half-spaceAug 28 2012Sep 17 2012We study the directed polymer with fixed endpoints near an absorbing wall, in the continuum and in presence of disorder, equivalent to the KPZ equation on the half space with droplet initial conditions. From a Bethe Ansatz solution of the equivalent attractive ... More
Exact renormalization group and applications to disordered problems: part IJun 04 2000We develop a systematic multi-local expansion of the Polchinski-Wilson exact renormalization group (ERG) equation. Integrating out explicitly the non local interactions, we reduce the ERG equation obeyed by the full interaction functional to a flow equation ... More
Glass phase of two-dimensional triangular elastic lattices with disorderNov 21 1996We 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 ... More
Aging and diffusion in low dimensional environmentsMay 24 1997We 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 ... More
Disorder induced transitions in layered Coulomb gases and application to flux lattices in superconductorsOct 01 2004Oct 02 2004A layered system of charges with logarithmic interaction parallel to the layers and random dipoles in each layer is studied via a variational method and an energy rationale. These methods reproduce the known phase diagram for a single layer where charges ... More
Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-lineMay 14 2019We consider the Kardar-Parisi-Zhang (KPZ) for the stochastic growth of an interface of height $h(x,t)$ on the positive half line with boundary condition $\partial_x h(x,t)|_{x=0}=A$. It is equivalent to a continuum directed polymer (DP) in a random potential ... More
Simple derivation of the $(- λH)^{5/2}$ tail for the 1D KPZ equationFeb 23 2018We study the long-time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimensions for the Brownian and droplet initial conditions and present a simple derivation of the tail of the large deviations of the height on the negative side $\lambda ... More
Linear statistics and pushed Coulomb gas at the edge of beta random matrices: four paths to large deviationsNov 01 2018The Airy$_\beta$ point process, $a_i \equiv N^{2/3} (\lambda_i-2)$, describes the eigenvalues $\lambda_i$ at the edge of the Gaussian $\beta$ ensembles of random matrices for large matrix size $N \to \infty$. We study the probability distribution function ... More
Replica Bethe Ansatz solution to the Kardar-Parisi-Zhang equation on the half-lineMay 14 2019May 17 2019We consider the Kardar-Parisi-Zhang (KPZ) for the stochastic growth of an interface of height $h(x,t)$ on the positive half line with boundary condition $\partial_x h(x,t)|_{x=0}=A$. It is equivalent to a continuum directed polymer (DP) in a random potential ... More
Topological transitions and freezing in XY models and Coulomb gases with quenched disorder: renormalization via traveling wavesAug 24 1999We study the two dimensional XY model with quenched random phases and its Coulomb gas formulation. A novel renormalization group (RG) method is developed which allows to study perturbatively the glassy low temperature XY phase and the transition at which ... More
Statics and Dynamics of Disordered Elastic SystemsMay 11 1997We 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 ... More
Extreme value statistics from the Real Space Renormalization Group: Brownian Motion, Bessel Processes and Continuous Time Random WalksOct 26 2009We use the Real Space Renormalization Group (RSRG) method to study extreme value statistics for a variety of Brownian motions, free or constrained such as the Brownian bridge, excursion, meander and reflected bridge, recovering some standard results, ... More
Broad relaxation spectrum and the field theory of glassy dynamics for pinned elastic systemsDec 13 2003We study thermally activated, low temperature equilibrium dynamics of elastic systems pinned by disorder using one loop functional renormalization group (FRG). Through a series of increasingly complete approximations, we investigate how the field theory ... More
Field theory of statics and dynamics of glasses: rare events and barrier distributionsMay 16 2002We study thermally activated dynamics using functional renormalization within the field theory of randomly pinned elastic systems, a prototype for glasses. It appears through an essentially non-perturbative boundary layer in the running effective action, ... More
The KPZ equation with flat initial condition and the directed polymer with one free endApr 12 2012We study the directed polymer (DP) of length $t$ in a random potential in dimension 1+1 in the continuum limit, with one end fixed and one end free. This maps onto the Kardar-Parisi-Zhang growth equation in time $t$, with flat initial conditions. We use ... More
An exact solution for the KPZ equation with flat initial conditionsApr 11 2011We provide the first exact calculation of the height distribution at arbitrary time $t$ of the continuum KPZ growth equation in one dimension with flat initial conditions. We use the mapping onto a directed polymer (DP) with one end fixed, one free, and ... More
Aging in the glass phase of a 2D random periodic elastic systemMar 16 2004Aug 05 2004Using RG we investigate the non-equilibrium relaxation of the (Cardy-Ostlund) 2D random Sine-Gordon model, which describes pinned arrays of lines. Its statics exhibits a marginal ($\theta=0$) glass phase for $T<T_g$ described by a line of fixed points. ... More
Anomalous elasticity, fluctuations and disorder in elastic membranesAug 18 2017Motivated by a freely suspended graphene and polymerized membranes in soft and biological matter we present a detailed study of a tensionless elastic sheet in the presence of thermal fluctuations and quenched disorder. The manuscript is based on an extensive ... More
Correlations between avalanches in the depinning dynamics of elastic interfacesApr 27 2019We study the correlations between avalanches in the depinning dynamics of elastic interfaces driven on a random substrate. In the mean field theory (the Brownian force model), it is known that the avalanches are uncorrelated. Here we obtain a simple field ... More
Large times off-equilibrium dynamics of a particle in a random potentialMay 24 1995We 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 ... More
Dynamical Transverse Meissner Effect and Transition in Moving Bose GlassOct 13 1999We study moving periodic structures in presence of correlated disorder using renormalisation group. We find that the effect of disorder persists at all velocities resulting at zero temperature in a Moving Bose Glass phase with transverse pinning. At non ... More
Systematic time expansion for the Kardar-Parisi-Zhang equation, linear statistics of the GUE at the edge and trapped fermionsAug 23 2018We present a systematic short time expansion for the generating function of the one point height probability distribution for the KPZ equation with droplet initial condition, which goes much beyond previous studies. The expansion is checked against a ... More
Crossing probability for directed polymers in random media: exact tail of the distributionNov 17 2015We study the probability $p \equiv p_\eta(t)$ that two directed polymers in a given random potential $\eta$ and with fixed and nearby endpoints, do not cross until time $t$. This probability is itself a random variable (over samples $\eta$) which, as ... More
Creep and depinning in disordered mediaFeb 18 2000Feb 21 2000Elastic systems driven in a disordered medium exhibit a depinning transition at zero temperature and a creep regime at finite temperature and slow drive $f$. We derive functional renormalization group equations which allow to describe in details the properties ... More
Comment on "Absence of the Mott Glass Phase in 1D Disordered Fermionic Systems"Sep 26 2008Comment on the paper "Absence of the Mott Glass Phase in 1D Disordered Fermionic Systems" by T. Nattermann, A. Petkovic, Z. Ristivojevic, and F. Schutze, Phys. Rev. Lett. 99, 186402 (2007).
Distribution of velocities in an avalancheApr 13 2011For a driven elastic object near depinning, we derive from first principles the distribution of instantaneous velocities in an avalanche. We prove that above the upper critical dimension, d >= d_uc, the n-times distribution of the center-of-mass velocity ... More
Size distributions of shocks and static avalanches from the Functional Renormalization GroupDec 10 2008Interfaces pinned by quenched disorder are often used to model jerky self-organized critical motion. We study static avalanches, or shocks, defined here as jumps between distinct global minima upon changing an external field. We show how the full statistics ... More
Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimensionOct 13 2005Oct 28 2005The functional RG for the random field and random anisotropy O(N) sigma-models is studied to two loop. The ferromagnetic/disordered (F/D) transition fixed point is found to next order in d=4+epsilon for N > N_c (N_c=2.8347408 for random field, N_c=9.44121 ... More
Polymers and manifolds in static random flows: a renormalization group studyAug 30 1998Jun 11 1999We study the dynamics of a polymer or a D-dimensional elastic manifold diffusing and convected in a non-potential static random flow (the ``randomly driven polymer model''). We find that short-range (SR) disorder is relevant for d < 4 for directed polymers ... More
Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-dimensional Random EnvironmentsOct 24 1997Dec 12 1997Sinai'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 ... More
Hessian spectrum at the global minimum of high-dimensional random landscapesJun 13 2018Jun 16 2018Using the replica method we calculate the mean spectral density of the Hessian matrix at the global minimum of a random $N \gg 1$ dimensional isotropic, translationally invariant Gaussian random landscape confined by a parabolic potential with fixed curvature ... More
Variable range hopping and quantum creep in one dimensionMar 12 2003We study the quantum non linear response to an applied electric field $E$ of a one dimensional pinned charge density wave or Luttinger liquid in presence of disorder. From an explicit construction of low lying metastable states and of bounce instanton ... More
Rings and boxes in dissipative environmentsJan 21 2011Jun 06 2011We study a particle on a ring in presence of a dissipative Caldeira-Leggett environment and derive its response to a DC field. We find, through a 2-loop renormalization group analysis, that a large dissipation parameter $\eta$ flows to a fixed point $\eta_R=\eta_c=\hbar/2\pi$. ... More
Specific Heat of Quantum Elastic Systems Pinned by DisorderNov 09 2004We present the detailed study of the thermodynamics of vibrational modes in disordered elastic systems such as the Bragg glass phase of lattices pinned by quenched impurities. Our study and our results are valid within the (mean field) replica Gaussian ... More
Specific heat of classical disordered elastic systemsJan 06 2003Jun 20 2003We study the thermodynamics of disordered elastic systems, applied to vortex lattices in the Bragg glass phase. Using the replica variational method we compute the specific heat of pinned vortons in the classical limit. We find that the contribution of ... More
Specific heat of the quantum Bragg GlassDec 12 2002Jun 18 2003We study the thermodynamics of the vibrational modes of a lattice pinned by impurity disorder in the absence of topological defects (Bragg glass phase). Using a replica variational method we compute the specific heat $C_v$ in the quantum regime and find ... More
Two-time height distribution for 1D KPZ growth: the recent exact result and its tail via replicaApr 05 2018May 10 2018We consider the fluctuations in the stochastic growth of a one-dimensional interface of height $h(x,t)$ described by the Kardar-Parisi-Zhang (KPZ) universality class. We study the joint probability distribution function (JPDF) of the interface heights ... More
Manifolds pinned by a high-dimensional random landscape: Hessian at the global energy minimumMar 17 2019We consider an elastic manifold of internal dimension $d$ and length $L$ pinned in a $N$ dimensional random potential and confined by an additional parabolic potential of curvature $\mu$. We are interested in the mean spectral density $\rho(\lambda)$ ... More
Winding of planar gaussian processesApr 03 2009We consider a smooth, rotationally invariant, centered gaussian process in the plane, with arbitrary correlation matrix $C_{t t'}$. We study the winding angle $\phi_t$ around its center. We obtain a closed formula for the variance of the winding angle ... More
Rings and Coulomb boxes in dissipative environmentsJul 11 2012Nov 17 2012We study a particle on a ring in presence of a dissipative Caldeira-Leggett environment and derive its response to a DC field. We show how this non-equilibrium response is related to a flux averaged equilibrium response. We find, through a 2-loop renormalization ... More
Topology trivialization and large deviations for the minimum in the simplest random optimizationMar 29 2013Aug 01 2013Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N-1)- dimensional sphere is one of the simplest, yet paradigmatic problems in Optimization Theory known as the "trust region subproblem" ... More
First-principle derivation of static avalanche-size distributionNov 14 2011We study the energy minimization problem for an elastic interface in a random potential plus a quadratic well. As the position of the well is varied, the ground state undergoes jumps, called shocks or static avalanches. We introduce an efficient and systematic ... More
Fluctuation force exerted by a planar self-avoiding polymerDec 09 2008Using results from Schramm Loewner evolution (SLE), we give the expression of the fluctuation-induced force exerted by a polymer on a small impenetrable disk, in various 2-dimensional domain geometries. We generalize to two polymers and examine whether ... More
Derivation of the Functional Renormalization Group Beta-Function at order 1/N for Manifolds Pinned by DisorderJun 12 2004In an earlier publication, we have introduced a method to obtain, at large N, the effective action for d-dimensional manifolds in a N-dimensional disordered environment. This allowed to obtain the Functional Renormalization Group (FRG) equation for N=infinity ... More
Renormalization of pinned elastic systems: how does it work beyond one loop ?Jun 04 2000Oct 20 2000We study the field theories for pinned elastic systems at equilibrium and at depinning. Their $\beta$-functions differ to two loops by novel ``anomalous'' terms. At equilibrium we find a roughness $\zeta=0.20829804 \epsilon + 0.006858 \epsilon^2$ (random ... More
Stability of Random-Field and Random-Anisotropy Fixed Points at large NDec 13 2006In this note, we clarify the stability of the large-N functional RG fixed points of the order/disorder transition in the random-field (RF) and random-anisotropy (RA) O(N) models. We carefully distinguish between infinite N, and large but finite N. For ... More
Free-energy distribution of the directed polymer at high temperatureFeb 24 2010Mar 22 2010We study the directed polymer of length $t$ in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods. The universal regime of high temperature $T$ is described, upon scaling ... More
Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?Apr 15 2008We study the time evolution of quantum one-dimensional gapless systems evolving from initial states with a domain-wall. We generalize the path-integral imaginary time approach that together with boundary conformal field theory allows to derive the time ... More
The universal high temperature regime of pinned elastic objectsJun 03 2010We study the high temperature regime within the glass phase of an elastic object with short ranged disorder. In that regime we argue that the scaling functions of any observable are described by a continuum model with a $\delta$-correlated disorder and ... More
Glassy behaviour in disordered systems with non-relaxational dynamicsJun 10 1996We 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 ... More
Universal distribution of threshold forces at the depinning transitionJul 10 2006We study the distribution of threshold forces at the depinning transition for an elastic system of finite size, driven by an external force in a disordered medium at zero temperature. Using the functional renormalization group (FRG) technique, we compute ... More
Revisiting Directed Polymers with heavy-tailed disorderNov 05 2014In this mostly numerical study, we revisit the statistical properties of the ground state of a directed polymer in a $d=1+1$ "hilly" disorder landscape, i.e. when the quenched disorder has power-law tails. When disorder is Gaussian, the polymer minimizes ... More
Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal $1/f$ noiseJul 19 2012Dec 07 2012To understand the sample-to-sample fluctuations in disorder-generated multifractal patterns we investigate analytically as well as numerically the statistics of high values of the simplest model - the ideal periodic $1/f$ Gaussian noise. By employing ... More
Statistical Mechanics of Logarithmic REM: Duality, Freezing and Extreme Value Statistics of $1/f$ Noises generated by Gaussian Free FieldsJul 14 2009Oct 19 2009We compute the distribution of the partition functions for a class of one-dimensional Random Energy Models (REM) with logarithmically correlated random potential, above and at the glass transition temperature. The random potential sequences represent ... More
Superfluid/Bose-glass transition in one dimensionApr 02 2014Sep 24 2014We consider a one-dimensional system of interacting bosons in a random potential. At zero temperature, it can be either in the superfluid or in the insulating phase. We study the transition at weak disorder and moderate interaction. Using a systematic ... More
Log-correlated Random Energy Models with extensive free energy fluctuations: pathologies caused by rare events as signatures of phase transitionsDec 16 2017Dec 19 2017We address systematically an apparent non-physical behavior of the free energy moment generating function for several instances of the logarithmically correlated models: the Fractional Brownian Motion with Hurst index $H = 0$ (fBm0) (and its bridge version), ... More
Dynamics of particles and manifolds in a quenched random force fieldDec 09 1996We 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 $\zeta$ and ... More
Universal correlations between shocks in the ground state of elastic interfaces in disordered mediaApr 19 2016Jul 26 2016The ground state of an elastic interface in a disordered medium undergoes collective jumps upon variation of external parameters. These mesoscopic jumps are called shocks, or static avalanches. Submitting the interface to a parabolic potential centered ... More
Spatial shape of avalanches in the Brownian force modelApr 21 2015We study the Brownian force model (BFM), a solvable model of avalanche statistics for an interface, in a general discrete setting. The BFM describes the overdamped motion of elastically coupled particles driven by a parabolic well in independent Brownian ... More
Liouville field theory and log-correlated Random Energy ModelsNov 07 2016An exact mapping is established between the $c\geq25$ Liouville field theory (LFT) and the Gibbs measure statistics of a thermal particle in a 2D Gaussian Free Field plus a logarithmic confining potential. The probability distribution of the position ... More
Genuine localisation transition in a long-range hopping modelJul 14 2016We introduce and study a new Banded Random Matrix model describing sparse, long range quantum hopping in one dimension. Using a series of analytic arguments, numerical simulations, and a mapping to a long range epidemics model, we establish the phase ... More
Freezing Transition in Decaying Burgers Turbulence and Random Matrix DualitiesApr 28 2010Jul 13 2010We reveal a phase transition with decreasing viscosity $\nu$ at \nu=\nu_c>0 in one-dimensional decaying Burgers turbulence with a power-law correlated random profile of Gaussian-distributed initial velocities <v(x,0)v(x',0)>\sim|x-x'|^{-2}. The low-viscosity ... More
Nonstationary dynamics of the Alessandro-Beatrice-Bertotti-Montorsi modelDec 29 2011May 17 2012We obtain an exact solution for the motion of a particle driven by a spring in a Brownian random-force landscape, the Alessandro-Beatrice-Bertotti-Montorsi (ABBM) model. Many experiments on quasi-static driving of elastic interfaces (Barkhausen noise ... More
Depinning in a two-layer model of plastic flowDec 30 2007We study a model of two layers, each consisting of a d-dimensional elastic object driven over a random substrate, and mutually interacting through a viscous coupling. For this model, the mean-field theory (i.e. a fully connected model) predicts a transition ... More
Super-rough phase of the random-phase sine-Gordon model: Two-loop resultsApr 27 2012Aug 01 2012We consider the two-dimensional random-phase sine-Gordon and study the vicinity of its glass transition temperature $T_c$, in an expansion in small $\tau=(T_c-T)/T_c$, where $T$ denotes the temperature. We derive renormalization group equations in cubic ... More
Statistics of static avalanches in a random pinning landscapeMar 07 2008We study the minimum-energy configuration of a d-dimensional elastic interface in a random potential tied to a harmonic spring. As a function of the spring position, the center of mass of the interface changes in discrete jumps, also called shocks or ... More
Exact form of the exponential correlation function in the glassy super-rough phaseApr 16 2013Jul 07 2013We consider the random-phase sine-Gordon model in two dimensions. It describes two-dimensional elastic systems with random periodic disorder, such as pinned flux-line arrays, random field XY models, and surfaces of disordered crystals. The model exhibits ... More
Multicritical edge statistics for the momenta of fermions in non-harmonic trapsFeb 18 2018We compute the joint statistics of the momenta $p_i$ of $N$ non-interacting fermions in a trap, near the Fermi edge, with a particular focus on the largest one $p_{\max}$. For a $1d$ harmonic trap, momenta and positions play a symmetric role and hence, ... More