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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

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

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

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

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

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

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

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

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

Functional Renormalization for pinned elastic systems away from their steady statesJan 10 2005Using one loop functional RG we study two problems of pinned elastic systems away from their equilibrium or steady states. The critical regime of the depinning transition is investigated starting from a flat initial condition. It exhibits non trivial ... More

Exact multilocal renormalization on the effective action : application to the random sine Gordon model statics and non-equilibrium dynamicsApr 22 2003We extend the exact multilocal renormalization group (RG) method to study the flow of the effective action functional. This important physical quantity satisfies an exact RG equation which is then expanded in multilocal components. Integrating the nonlocal ... 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

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

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

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

Low-temperature properties of some disordered systems from the statistical properties of nearly degenerate two-level excitationsJul 12 2004The thermal fluctuations that exist at very low temperature in disordered systems are often attributed to the existence of some two-level excitations. In this paper, we revisit this question via the explicit studies of the following 1D models (i) a particle ... More

Reaction Diffusion Models in One Dimension with DisorderJan 27 1999We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random local bias ... 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

Exact solution for a random walk in a time-dependent 1D random environment: the point-to-point Beta polymerMay 24 2016We consider the Beta polymer, an exactly solvable model of directed polymer on the square lattice, introduced by Barraquand and Corwin. We study the statistical properties of its point to point partition sum. The problem is equivalent to a model of a ... 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

Energy dynamics in the Sinai modelJun 04 2002We study the time dependent potential energy $W(t)=U(x(0)) - U(x(t))$ of a particle diffusing in a one dimensional random force field (the Sinai model). Using the real space renormalization group method (RSRG), we obtain the exact large time limit of ... 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

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

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

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

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

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

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

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

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

Creep in One Dimension and Phenomenological Theory of Glass DynamicsJan 29 1995Jul 28 1995The 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 ... 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

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

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

An exact mapping of the stochastic field theory for Manna sandpiles to interfaces in random mediaOct 07 2014We show that the stochastic field theory for directed percolation in presence of an additional conservation law (the C-DP class) can be mapped exactly to the continuum theory for the depinning of an elastic interface in short-range correlated quenched ... More

Driven particle in a random landscape: disorder correlator, avalanche distribution and extreme value statistics of recordsAug 23 2008We review how the renormalized force correlator Delta(u), the function computed in the functional RG field theory, can be measured directly in numerics and experiments on the dynamics of elastic manifolds in presence of pinning disorder. We show how this ... More

Functional renormalization group at large N for random manifoldsSep 11 2001We introduce a method, based on an exact calculation of the effective action at large N, to bridge the gap between mean field theory and renormalization in complex systems. We apply it to a d-dimensional manifold in a random potential for large embedding ... More

Glassy trapping of manifolds in nonpotential random flowsAug 15 1997We 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 ... More

How to measure Functional RG fixed-point functions for dynamics and at depinningOct 18 2006We show how the renormalized force correlator Delta(u), the function computed in the functional RG (FRG) field theory, can be measured directly in numerics and experiments on the dynamics of elastic manifolds in presence of pinning disorder. For equilibrium ... More

Functional Renormalization Group at Large N for Disordered Elastic Systems, and Relation to Replica Symmetry BreakingMay 28 2003We study the replica field theory which describes the pinning of elastic manifolds of arbitrary internal dimension d in a random potential, with the aim of bridging the gap between mean field and renormalization theory. The full effective action is computed ... More

Moments of the position of the maximum for GUE characteristic polynomials and for log-correlated Gaussian processesNov 13 2015Jun 11 2016We study three instances of log-correlated processes on the interval: the logarithm of the Gaussian unitary ensemble (GUE) characteristic polynomial, the Gaussian log-correlated potential in presence of edge charges, and the Fractional Brownian motion ... More

Mutually avoiding paths in random media and largests eigenvalues of random matricesJun 27 2016Recently, it was shown that the probability distribution function (PDF) of the free energy of a single continuum directed polymer (DP) in a random potential, equivalently of the height of a growing interface described by the Kardar-Parisi-Zhang (KPZ) ... More

The crossing probability for directed polymers in random mediaMay 18 2015Apr 30 2016We study the probability that two directed polymers in the same random potential do not intersect. We use the replica method to map the problem onto the attractive Lieb-Liniger model with generalized statistics between particles. We obtain analytical ... 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

Genuine localisation transition in a long-range hopping modelJul 14 2016Oct 20 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

Functional Renormalization Group and the Field Theory of Disordered Elastic SystemsApr 27 2003We study elastic systems such as interfaces or lattices, pinned by quenched disorder. To escape triviality as a result of ``dimensional reduction'', we use the functional renormalization group. Difficulties arise in the calculation of the renormalization ... More

Functional renormalization-group approach to decaying turbulenceDec 10 2012We reconsider the functional renormalization-group (FRG) approach to decaying Burgers turbulence, and extend it to decaying Navier-Stokes and Surface-Quasi-Geostrophic turbulence. The method is based on a renormalized small-time expansion, equivalent ... More

Field theory conjecture for loop-erased random walksMar 16 2008Nov 24 2008We give evidence that the functional renormalization group (FRG), developed to study disordered systems, may provide a field theoretic description for the loop-erased random walk (LERW), allowing to compute its fractal dimension in a systematic expansion ... More

Exact short-time height distribution in 1D KPZ equation and edge fermions at high temperatureMar 10 2016We consider the early time regime of the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimensions in curved (or droplet) geometry. We show that for short time $t$, the probability distribution $P(H,t)$ of the height $H$ at a given point $x$ takes the scaling ... More