arXiv subjects

J. -P. Bouchaud

Publications and source records attributed to J. -P. Bouchaud.

At least 19 recordsLinked to original sources

arXiv2017

Unifying different interpretations of the nonlinear response in glass-forming liquids

This work aims at reconsidering several interpretations coexisting in the recent literature concerning non-linear susceptibilities in supercooled liquids. We present experimental results on glycerol and propylene carbonate showing that the three independent cubic susceptibilities have very similar frequency and temperature dependences, both for their amplitudes and phases. This strongly suggests a unique physical mechanism responsible for the growth of these non-linear susceptibilities. We show that the framework proposed by two of us [BB, Phys. Rev. B 72, 064204 (2005)], where the growth of non-linear susceptibilities is intimately related to the growth of "glassy domains", accounts for all the salient experimental features. We then review several complementary and/or alternative models, and show that the notion of cooperatively rearranging glassy domains is a key (implicit or explicit) ingredient to all of them. This paves the way for future experiments which should deepen our understanding of glasses.

cond-mat.dis-nn↗

arXiv2016

Fifth-order susceptibility unveils growth of thermodynamic amorphous order in glass-formers

Glasses are ubiquitous in daily life and technology. However the microscopic mechanisms generating this state of matter remain subject to debate: Glasses are considered either as merely hyper-viscous liquids or as resulting from a genuine thermodynamic phase transition towards a rigid state. We show that third- and fifth-order susceptibilities provide a definite answer to this longstanding controversy. Performing the corresponding high-precision nonlinear dielectric experiments for supercooled glycerol and propylene carbonate, we find strong support for theories based upon thermodynamic amorphous order. Moreover, when lowering temperature, we find that the growing transient domains are compact - that is their fractal dimension d_f = 3. The glass transition may thus represent a class of critical phenomena different from canonical second-order phase transitions for which d_f < 3.

cond-mat.dis-nn↗

arXiv2014

Slow decay of impact in equity markets

Using a proprietary dataset of meta-orders and prediction signals, and assuming a quasi-linear impact model, we deconvolve market impact from past correlated trades and a predictable return component to elicit the temporal dependence of the market impact of a single daily meta-order, over a ten day horizon in various equity markets. We find that the impact of single meta-orders is to a first approximation universal and slowly decays to zero (or to a small value), possibly as a power-law. We show that auto-correlated order-flows and trade information contents fully accounts for the apparent plateau observed in the raw data. We discuss the possible bias introduced by the quasi-linear assumption.

q-fin.TR↗

arXiv2013

A Fokker-Planck description for the queue dynamics of large tick stocks

Motivated by empirical data, we develop a statistical description of the queue dynamics for large tick assets based on a two-dimensional Fokker-Planck (diffusion) equation, that explicitly includes state dependence, i.e. the fact that the drift and diffusion depends on the volume present on both sides of the spread. "Jump" events, corresponding to sudden changes of the best limit price, must also be included as birth-death terms in the Fokker-Planck equation. All quantities involved in the equation can be calibrated using high-frequency data on best quotes. One of our central finding is the the dynamical process is approximately scale invariant, i.e., the only relevant variable is the ratio of the current volume in the queue to its average value. While the latter shows intraday seasonalities and strong variability across stocks and time periods, the dynamics of the rescaled volumes is universal. In terms of rescaled volumes, we found that the drift has a complex two-dimensional structure, which is a sum of a gradient contribution and a rotational contribution, both stable across stocks and time. This drift term is entirely responsible for the dynamical correlations between the ask queue and the bid queue.

q-fin.TR↗

arXiv2012

We've walked a million miles for one of these smiles

We derive a new, exact and transparent expansion for option smiles, which lends itself both to analytical approximation and, perhaps more importantly, to congenial numerical treatments. We show that the skew and the curvature of the smile can be computed as exotic options, for which the Hedged Monte Carlo method is particularly well suited. When applied to options on the S&P index, we find that the skew and the curvature of the smile are very poorly reproduced by the standard Edgeworth (cumulant) expansion. Most notably, the relation between the skew and the skewness is inverted at small and large vols, a feature that none of the model studied so far is able to reproduce. Furthermore, the around-the-money curvature of the smile is found to be very small, in stark contrast with the highly kurtic nature of the returns.

q-fin.PR↗

arXiv2010

Evidence of deep water penetration in silica during stress corrosion fracture

We measure the thickness of the heavy water layer trapped under the stress corrosion fracture surface of silica using neutron reflectivity experiments. We show that the penetration depth is 65-85 ångströms, suggesting the presence of a damaged zone of $\approx$ 100 ångströms extending ahead of the crack tip during its propagation. This estimate of the size of the damaged zone is compatible with other recent results.

cond-mat.mtrl-sci↗

arXiv2009

Mode-Coupling as a Landau Theory of the Glass Transition

We derive the Mode Coupling Theory (MCT) of the glass transition as a Landau theory, formulated as an expansion of the exact dynamical equations in the difference between the correlation function and its plateau value. This sheds light on the universality of MCT predictions. While our expansion generates higher order non-local corrections that modify the standard MCT equations, we find that the square root singularity of the order parameter, the scaling function in the βregime and the functional relation between the exponents defining the αand βtimescales are universal and left intact by these corrections.

cond-mat.stat-mech↗

arXiv2008

Thermodynamic signature of growing amorphous order in glass-forming liquids

Although several theories relate the steep slowdown of glass formers to increasing spatial correlations of some sort, standard static correlation functions show no evidence for this. We present results that reveal for the first time a qualitative thermodynamic difference between the high temperature and deeply supercooled equilibrium glass-forming liquid: the influence of boundary conditions propagates into the bulk over larger and larger lengthscales upon cooling, and, as this static correlation length grows, the influence decays nonexponentially. Increasingly long-range susceptibility to boundary conditions is expected within the random firt-order theory (RFOT) of the glass transition, but a quantitative account of our numerical results requires a generalization of RFOT where the surface tension between states fluctuates.

cond-mat.dis-nn↗

arXiv2008

Critical scaling and heterogeneous superdiffusion across the jamming/rigidity transition of a granular glass

The dynamical properties of a dense horizontally vibrated bidisperse granular monolayer are experimentally investigated. The quench protocol produces states with a frozen structure of the assembly, but the remaining degrees of freedom associated with contact dynamics control the appearance of macroscopic rigidity. We provide decisive experimental evidence that this transition is a critical phenomenon, with increasingly collective and heterogeneous rearrangements occurring at length scales much smaller than the grains' diameter, presumably reflecting the contact force network fluctuations. Dynamical correlation time and length scales soar on both sides of the transition, as the volume fraction varies over a remarkably tiny range ($δϕ/ϕ\sim 10^{-3}$). We characterize the motion of individual grains, which becomes super-diffusive at the jamming transition $ϕ_J$, signaling long-ranged temporal correlations. Correspondingly, the system exhibits long-ranged four-point dynamical correlations in space that obey critical scaling at the transition density.

cond-mat.soft↗

arXiv2008

Spin glass behavior in an interacting gamma-Fe2O3 nanoparticle system

In this paper we investigate the superspin glass behavior of a concentrated assembly of interacting maghemite nanoparticles and compare it to that of canonical atomic spin glass systems. ac versus temperature and frequency measurements show evidence of a superspin glass transition taking place at low temperature. In order to fully characterize the superspin glass phase, the aging behavior of both the thermo-remanent magnetization (TRM) and ac susceptibility has been investigated. It is shown that the scaling laws obeyed by superspin glasses and atomic spin glasses are essentially the same, after subtraction of a superparamagnetic contribution from the superspin glass response functions. Finally, we discuss a possible origin of this superparamagnetic contribution in terms of dilute spin glass models.

cond-mat.dis-nn↗

arXiv2004

Aging, rejuvenation and memory phenomena in spin glasses

In this paper, we review several important features of the out-of-equilibrium dynamics of spin glasses. Starting with the simplest experiments, we discuss the scaling laws used to describe the isothermal aging observed in spin glasses after a quench down to the low temperature phase. We report in particular new results on the sub-aging behaviour of spin glasses. We then discuss the rejuvenation and memory effects observed when a spin glass is submitted to temperature variations during aging, from the point of view of both energy landscape pictures and of real space pictures. We highlight the fact that both approaches point out the necessity of hierarchical processes involved in aging. Finally, we report an investigation of the effect of small temperature variations on aging in spin glass samples with various anisotropies which indicates that this hierarchy depends on the spin anisotropy.

cond-mat.dis-nn↗

arXiv2004

On the Adam-Gibbs-Wolynes scenario for the viscosity increase in glasses

We reformulate the interpretation of the mean-field glass transition scenario for finite dimensional systems, proposed by Wolynes and collaborators. This allows us to establish clearly a temperature dependent length xi* above which the mean-field glass transition picture has to be modified. We argue in favor of the mosaic state introduced by Wolynes and collaborators, which leads to the Adam-Gibbs relation between the viscosity and configurational entropy of glass forming liquids. Our argument is a mixture of thermodynamics and kinetics, partly inspired by the Random Energy Model: small clusters of particles are thermodynamically frozen in low energy states, whereas large clusters are kinetically frozen by large activation energies. The relevant relaxation time is that of the smallest `liquid' clusters. Some physical consequences are discussed.

cond-mat.stat-mech↗

arXiv2004

Random walks, liquidity molasses and critical response in financial markets

Stock prices are observed to be random walks in time despite a strong, long term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long ranged fluctuations in liquidity, with an otherwise permanent market impact, challenging the scenario proposed in Quantitative Finance 4, 176 (2004), where the impact is *transient*, with a power-law decay in time. The exponent of this decay is precisely tuned to a critical value, ensuring simultaneously that prices are diffusive on long time scales and that the response function is nearly constant. We provide new analysis of empirical data that confirm and make more precise our previous claims. We show that the power-law decay of the bare impact function comes both from an excess flow of limit order opposite to the market order flow, and to a systematic anti-correlation of the bid-ask motion between trades, two effects that create a `liquidity molasses' which dampens market volatility.

cond-mat.other↗

arXiv2004

Spin Anisotropy and Slow Dynamics in Spin Glasses

We report on an extensive study of the influence of spin anisotropy on spin glass aging dynamics. New temperature cycle experiments allow us to compare quantitatively the memory effect in four Heisenberg spin glasses with various degrees of random anisotropy and one Ising spin glass. The sharpness of the memory effect appears to decrease continuously with the spin anisotropy. Besides, the spin glass coherence length is determined by magnetic field change experiments for the first time in the Ising sample. For three representative samples, from Heisenberg to Ising spin glasses, we can consistently account for both sets of experiments (temperature cycle and magnetic field change) using a single expression for the growth of the coherence length with time.

cond-mat.dis-nn↗

arXiv2003

Energy exponents and corrections to scaling in Ising spin glasses

We study the probability distribution P(E) of the ground state energy E in various Ising spin glasses. In most models, P(E) seems to become Gaussian with a variance growing as the system's volume V. Exceptions include the Sherrington-Kirkpatrick model (where the variance grows more slowly, perhaps as the square root of the volume), and mean field diluted spin glasses having +/-J couplings. We also find that the corrections to the extensive part of the disorder averaged energy grow as a power of the system size; for finite dimensional lattices, this exponent is equal, within numerical precision, to the domain-wall exponent theta_DW. We also show how a systematic expansion of theta_DW in powers of exp(-d) can be obtained for Migdal-Kadanoff lattices. Some physical arguments are given to rationalize our findings.

cond-mat.dis-nn↗

arXiv2003

The Kovacs effect in model glasses

We discuss the `memory effect' discovered in the 60's by Kovacs in temperature shift experiments on glassy polymers, where the volume (or energy) displays a non monotonous time behaviour. This effect is generic and is observed on a variety of different glassy systems (including granular materials). The aim of this paper is to discuss whether some microscopic information can be extracted from a quantitative analysis of the `Kovacs hump'. We study analytically two families of theoretical models: domain growth and traps, for which detailed predictions of the shape of the hump can be obtained. Qualitatively, the Kovacs effect reflects the heterogeneity of the system: its description requires to deal not only with averages but with a full probability distribution (of domain sizes or of relaxation times). We end by some suggestions for a quantitative analysis of experimental results.

cond-mat.dis-nn↗

arXiv2003

Local excitations of a spin glass in a magnetic field

We study the minimum energy clusters (MEC) above the ground state for the 3-d Edwards-Anderson Ising spin glass in a magnetic field. For fields B below 0.4, we find that the field has almost no effect on the excitations that we can probe, of volume V <= 64. As found previously for B=0, their energies decrease with V, and their magnetization remains very small (even slightly negative). For larger fields, both the MEC energy and magnetization grow with V, as expected in a paramagnetic phase. However, all results appear to scale as BV (instead of the B sqrt(V) expected from droplet arguments), suggesting that the spin glass phase is destroyed by any small field. Finally, the geometry of the MEC is completely insensitive to the field, giving further credence that they are lattice animals, in the presence or the absence of a field.

cond-mat.dis-nn↗

arXiv2003

Linear and non linear response in the aging regime of the 1D trap model

We investigate the behaviour of the response function in the one dimensional trap model using scaling arguments that we confirm by numerical simulations. We study the average position of the random walk at time tw+t given that a small bias h is applied at time tw. Several scaling regimes are found, depending on the relative values of t, tw and h. Comparison with the diffusive motion in the absence of bias allows us to show that the fluctuation dissipation relation is, in this case, valid even in the aging regime.

cond-mat.dis-nn↗