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Hugues Chaté

Publications and source records attributed to Hugues Chaté.

At least 73 records · Page 4Linked to original sources
arXiv2012

Finite scale singularity in the renormalization group flow of a reaction-diffusion system

We study the nonequilibrium critical behavior of the pair contact process with diffusion (PCPD) by means of nonperturbative functional renormalization group techniques. We show that usual perturbation theory fails because the effective potential develops a nonanalyticity at a finite length scale: Perturbatively forbidden terms are dynamically generated and the flow can be continued once they are taken into account. Our results suggest that the critical behavior of PCPD can be either in the directed percolation or in a new (conjugated) universality class.

cond-mat.stat-mech↗
arXiv2012

Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications

We present an analytical method, rooted in the non-perturbative renormalization group, that allows one to calculate the critical exponents and the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth equation in all its different regimes, including the strong-coupling one. We analyze the symmetries of the KPZ problem and derive an approximation scheme that satisfies the linearly realized ones. We implement this scheme at the minimal order in the response field, and show that it yields a complete, qualitatively correct phase diagram in all dimensions, with reasonable values for the critical exponents in physical dimensions. We also compute in one dimension the full (momentum and frequency dependent) correlation function, and the associated universal scaling functions. We find an excellent quantitative agreement with the exact results from Praehofer and Spohn (J. Stat. Phys. 115 (2004)). We emphasize that all these results, which can be systematically improved, are obtained with sole input the bare action and its symmetries, without further assumptions on the existence of scaling or on the form of the scaling function.

cond-mat.stat-mech↗
arXiv2012

Simple and faithful nonlinear field equations for aligning self-propelled rods

We derive a set of minimal yet complete nonlinear field equations describing the collective properties of self-propelled rods from a simple microscopic starting point, the Vicsek model with nematic alignment. Analysis of their linear and nonlinear dynamics shows good agreement with the original microscopic model. In particular, we derive an explicit expression for the fronts forming density-segregated, banded solutions, allowing us to develop a more complete analytic picture of the problem at the nonlinear level.

cond-mat.soft↗
arXiv2012

Competing ferromagnetic and nematic alignment in self-propelled polar particles

We study a Vicsek-style model of self-propelled particles where ferromagnetic and nematic alignment compete in both the usual "metric" version and in the "metric-free" case where a particle interacts with its Voronoi neighbors. We show that the phase diagram of this out-of-equilibrium XY model is similar to that of its equilibrium counterpart: the properties of the fully-nematic model, studied before in [F. Ginelli, F. Peruani, M. Baer, and H. Chaté, Phys. Rev. Lett. 104, 184502 (2010)], are thus robust to the introduction of a modest bias of interactions towards ferromagnetic alignment. The direct transitions between polar and nematic ordered phases are shown to be discontinuous in the metric case, and continuous, belonging to the Ising universality class, in the metric-free version.

cond-mat.soft↗
arXiv2012

Continuous theory of active matter systems with metric-free interactions

We derive a hydrodynamic description of metric-free active matter: starting from self-propelled particles aligning with neighbors defined by "topological" rules, not metric zones, -a situation advocated recently to be relevant for bird flocks, fish schools, and crowds- we use a kinetic approach to obtain well-controlled nonlinear field equations. We show that the density-independent collision rate per particle characteristic of topological interactions suppresses the linear instability of the homogeneous ordered phase and the nonlinear density segregation generically present near threshold in metric models, in agreement with microscopic simulations.

cond-mat.soft↗
arXiv2012

Vibrated polar disks: spontaneous motion, binary collisions, and collective dynamics

We study the spontaneous motion, binary collisions, and collective dynamics of "polar disks", i.e. purpose-built particles which, when vibrated between two horizontal plates, move coherently along a direction strongly correlated to their intrinsic polarity. The motion of our particles, although nominally three-dimensional and complicated, is well accounted for by a two-dimensional persistent random walk. Their binary collisions are spatiotemporally extended events during which multiple actual collisions happen, yielding a weak average effective alignment. We show that this well-controlled, "dry active matter" system can display collective motion with orientationally-ordered regions of the order of the system size. We provide evidence of strong number density in the most ordered regimes observed. These results are discussed in the light of the limitations of our system, notably those due to the inevitable presence of walls.

cond-mat.soft↗
arXiv2011

General framework of the non-perturbative renormalization group for non-equilibrium steady states

This paper is devoted to presenting in detail the non-perturbative renormalization group (NPRG) formalism to investigate out-of-equilibrium systems and critical dynamics in statistical physics. The general NPRG framework for studying non-equilibrium steady states in stochastic models is expounded and fundamental technicalities are stressed, mainly regarding the role of causality and of Ito's discretization. We analyze the consequences of Ito's prescription in the NPRG framework and eventually provide an adequate regularization to encode them automatically. Besides, we show how to build a supersymmetric NPRG formalism with emphasis on time-reversal symmetric problems, whose supersymmetric structure allows for a particularly simple implementation of NPRG in which causality issues are transparent. We illustrate the two approaches on the example of Model A within the derivative expansion approximation at order two, and check that they yield identical results.

cond-mat.stat-mech↗
arXiv2011

Hyperbolic decoupling of tangent space and effective dimension of dissipative systems

We show, using covariant Lyapunov vectors, that the tangent space of spatially-extended dissipative systems is split into two hyperbolically decoupled subspaces: one comprising a finite number of frequently entangled "physical" modes, which carry the physically relevant information of the trajectory, and a residual set of strongly decaying "spurious" modes. The decoupling of the physical and spurious subspaces is defined by the absence of tangencies between them and found to take place generally; we find evidence in partial differential equations in one and two spatial dimensions and even in lattices of coupled maps or oscillators. We conjecture that the physical modes may constitute a local linear description of the inertial manifold at any point in the global attractor.

nlin.CD↗
arXiv2011

Extensive and Sub-Extensive Chaos in Globally-Coupled Dynamical Systems

Using a combination of analytical and numerical techniques, we show that chaos in globally-coupled identical dynamical systems, be they dissipative or Hamiltonian, is both extensive and sub-extensive: their spectrum of Lyapunov exponents is asymptotically flat (thus extensive) at the value $λ_0$ given by a single unit forced by the mean-field, but sandwiched between sub-extensive bands containing typically $\mathcal{O}(\log N)$ exponents whose values vary as $λ\simeq λ_\infty + c/\log N$ with $λ_\infty \neq λ_0$.

nlin.CD↗
arXiv2010

Relevance of Metric-Free Interactions in Flocking Phenomena

We show that the collective properties of self-propelled particles aligning with their "topological" (Voronoi) neighbors are qualitatively different from those of usual models where metric interaction ranges are used. This relevance of metric-free interactions, shown in a minimal setting, indicate that realistic models for the cohesive motion of cells, bird flocks, and fish schools may have to incorporate them, as suggested by recent observations.

cond-mat.stat-mech↗
arXiv2010

Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation

We present a simple approximation of the non-perturbative renormalization group designed for the Kardar-Parisi-Zhang equation and show that it yields the correct phase diagram, including the strong-coupling phase with reasonable scaling exponent values in physical dimensions. We find indications of a possible qualitative change of behavior around $d=4$. We discuss how our approach can be systematically improved.

cond-mat.stat-mech↗
arXiv2009

Lyapunov analysis captures the collective dynamics of large chaotic systems

We show, using generic globally-coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting collectively on the trajectory. For globally-coupled maps, we show moreover a quantitative correspondence between the collective modes and some of the so-called Perron-Frobenius dynamics. Our results imply that the conventional definition of extensivity must be changed as soon as collective dynamics sets in.

nlin.CD↗
arXiv2009

Experimental realization of directed percolation criticality in turbulent liquid crystals

This is a comprehensive report on the phase transition between two turbulent states of electroconvection in nematic liquid crystals, which was recently found by the authors to be in the directed percolation (DP) universality class [K. A. Takeuchi et al., Phys. Rev. Lett. 99, 234503 (2007)]. We further investigate both static and dynamic critical behavior of this phase transition, measuring a total of 12 critical exponents, 5 scaling functions, and 8 scaling relations, all in full agreement with those characterizing the DP class in 2+1 dimensions. Developing an experimental technique to create a seed of topological-defect turbulence by pulse laser, we confirm in particular the rapidity symmetry, which is a basic but nontrivial consequence of the field-theoretic approach to DP. This provides the first clear experimental realization of this outstanding, truly out-of-equilibrium universality class, dominating most phase transitions into an absorbing state.

cond-mat.stat-mech↗
arXiv2008

Hyperbolicity and the effective dimension of spatially-extended dissipative systems

We show, using covariant Lyapunov vectors, that the chaotic solutions of spatially extended dissipative systems evolve within a manifold spanned by a finite number of physical modes hyperbolically isolated from a set of residual degrees of freedom, themselves individually isolated from each other. In the context of dissipative partial differential equations, our results imply that a faithful numerical integration needs to incorporate at least all physical modes and that increasing the resolution merely increases the number of isolated modes.

nlin.CD↗
arXiv2007

Collective motion of self-propelled particles interacting without cohesion

We present a comprehensive study of Vicsek-style self-propelled particle models in two and three space dimensions. The onset of collective motion in such stochastic models with only local alignment interactions is studied in detail and shown to be discontinuous (first-order like). The properties of the ordered, collectively moving phase are investigated. In a large domain of parameter space including the transition region, well-defined high-density and high-order propagating solitary structures are shown to dominate the dynamics. Far enough from the transition region, on the other hand, these objects are not present. A statistically-homogeneous ordered phase is then observed, which is characterized by anomalously-strong density fluctuations, superdiffusion, and strong intermittency.

cond-mat.stat-mech↗
arXiv2007

Directed percolation criticality in turbulent liquid crystals

We experimentally investigate the critical behavior of a phase transition between two topologically different turbulent states of electrohydrodynamic convection in nematic liquid crystals. The statistical properties of the observed spatiotemporal intermittency regimes are carefully determined, yielding a complete set of static critical exponents in full agreement with those defining the directed percolation class in (2+1) dimensions. This constitutes the first clear and comprehensive experimental evidence of an absorbing phase transition in this prominent non-equilibrium universality class.

cond-mat.stat-mech↗
arXiv2006

Non-perturbative Approach to Critical Dynamics

This paper is devoted to a non-perturbative renormalization group (NPRG) analysis of Model A, which stands as a paradigm for the study of critical dynamics. The NPRG formalism has appeared as a valuable theoretical tool to investigate non-equilibrium critical phenomena, yet the simplest -- and nontrivial -- models for critical dynamics have never been studied using NPRG techniques. In this paper we focus on Model A taking this opportunity to provide a pedagological introduction to NPRG methods for dynamical problems in statistical physics. The dynamical exponent $z$ is computed in $d=3$ and $d=2$ and is found in close agreement with results from other methods.

cond-mat.stat-mech↗