arXiv subjects

G. Biroli

Publications and source records attributed to G. Biroli.

At least 19 recordsLinked to original sources

arXiv2020

Dynamical Instantons and Activated Processes in Mean-Field Glass Models

We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure spherical $p$-spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process.

cond-mat.dis-nn↗

arXiv2018

Random-Field Ising like effective theory of the glass transition: I Mean-Field Models

In this paper and in the companion one we address the problem of identifying the effective theory that describes the statistics of the fluctuations of what is thought to be the relevant order parameter for glassy systems---the overlap field with an equilibrium reference configuration---close to the putative thermodynamic glass transition. Our starting point is the mean-field theory of glass formation which relies on the existence of a complex free-energy landscape with a multitude of metastable states. In this paper, we focus on archetypal mean-field models possessing this type of free-energy landscape and set up the framework to determine the exact effective theory. We show that the effective theory at the mean-field level is generically of the random-field + random-bond Ising type. We also discuss what are the main issues concerning the extension of our result to finite-dimensional systems. This extension is addressed in detail in the companion paper.

cond-mat.stat-mech↗

arXiv2018

Random Field Ising-like effective theory of the glass transition II: Finite Dimensional Models

As in the preceding paper we aim at identifying the effective theory that describes the fluctuations of the local overlap with an equilibrium reference configuration close to a putative thermodynamic glass transition. We focus here on the case of finite-dimensional glass-forming systems, in particular supercooled liquids. The main difficulty for going beyond the mean-field treatment comes from the presence of diverging point-to-set spatial correlations. We introduce a variational low-temperature approximation scheme that allows us to account, at least in part, for the effect of these correlations. The outcome is an effective theory for the overlap fluctuations in terms of a random-field + random-bond Ising model with additional, power-law decaying, pair and multi-body interactions generated by the point-to-set correlations. This theory is much more tractable than the original problem. We check the robustness of the approximation scheme by applying it to a fully connected model already studied in the companion paper. We discuss the physical implications of this mapping for glass-forming liquids and the possibility it offers to determine the presence or not of a finite-temperature thermodynamic glass transition.

cond-mat.stat-mech↗

arXiv2018

Comparing Dynamics: Deep Neural Networks versus Glassy Systems

We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are (1) the complexity of the loss landscape and of the dynamics within it, and (2) to what extent DNNs share similarities with glassy systems. Our findings, obtained for different architectures and datasets, suggest that during the training process the dynamics slows down because of an increasingly large number of flat directions. At large times, when the loss is approaching zero, the system diffuses at the bottom of the landscape. Despite some similarities with the dynamics of mean-field glassy systems, in particular, the absence of barrier crossing, we find distinctive dynamical behaviors in the two cases, showing that the statistical properties of the corresponding loss and energy landscapes are different. In contrast, when the network is under-parametrized we observe a typical glassy behavior, thus suggesting the existence of different phases depending on whether the network is under-parametrized or over-parametrized.

stat.ML↗

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↗

arXiv2015

Ultrafast dynamics of fluctuations in high-temperature superconductors far from equilibrium

Despite extensive work on high-temperature superconductors, the critical behavior of an incipient condensate has so far been studied exclusively under equilibrium conditions. Here, we excite Bi2Sr2CaCu2O8+d with a femtosecond laser pulse and monitor the subsequent nonequilibrium dynamics of the mid-infrared conductivity. Our data allow us to discriminate temperature regimes where superconductivity is either coherent, fluctuating or vanishingly small. Above the transition temperature Tc, we make the striking observation that the relaxation to equilibrium exhibits power-law dynamics and scaling behavior, both for optimally and underdoped superconductors. Our findings can in part be modeled using time-dependent Ginzburg-Landau theory and provide strong indication of universality in systems far from equilibrium.

cond-mat.supr-con↗

arXiv2013

Confinement as a tool to probe amorphous order

We study the effect of confinement on glassy liquids using Random First Order Transition theory as framework. We show that the characteristic length-scale above which confinement effects become negligible is related to the point-to-set length-scale introduced to measure the spatial extent of amorphous order in super-cooled liquids. By confining below this characteristic size, the system becomes a glass. Eventually, for very small sizes, the effect of the boundary is so strong that any collective glassy behavior is wiped out. We clarify similarities and differences between the physical behaviors induced by confinement and by pinning particles outside a spherical cavity (the protocol introduced to measure the point-to-set length). Finally, we discuss possible numerical and experimental tests of our predictions.

cond-mat.dis-nn↗

arXiv2012

Difference between level statistics, ergodicity and localization transitions on the Bethe lattice

We show that non-interacting disordered electrons on a Bethe lattice display a new intermediate phase which is delocalized but non-ergodic, i.e. it is characterized by Poisson instead of GOE statistics. The physical signature of this phase is a very heterogenous transport that proceeds over a few disorder dependent paths only. We show that the transition to the usual ergodic delocalized phase, which takes place for a disorder strength smaller than the one leading to the localization transition, is related to the freezing-glass transition of directed polymers in random media. The numerical study of level and eigenstate statistics, and of the singular properties of the probability distribution of the local density of states all support the existence of this new intermediate phase. Our results suggest that the localization transition may change nature in high dimensional systems.

cond-mat.dis-nn↗

arXiv2012

On the fragility of the mean-field scenario of structural glasses for finite-dimensional disordered spin models

At the mean-field level, on fully connected lattices, several disordered spin models have been shown to belong to the universality class of "structural glasses", with a "random first-order transition" (RFOT) characterized by a discontinuous jump of the order parameter and no latent heat. However, their behavior in finite dimensions is often drastically different, displaying either no glassiness at all or a conventional spin-glass transition. We clarify the physical reasons for this phenomenon and stress the unusual fragility of the RFOT to short-range fluctuations, associated e.g. with the mere existence of a finite number of neighbors. Accordingly, the solution of fully connected models is only predictive in very high dimension whereas, despite being also mean-field in character, the Bethe approximation provides valuable information on the behavior of finite-dimensional systems. We suggest that before embarking on a full-blown account of fluctuations on all scales through computer simulation or renormalization-group approach, models for structural glasses should first be tested for the effect of short-range fluctuations and we discuss ways to do it. Our results indicate that disordered spin models do not appear to pass the test and are therefore questionable models for investigating the glass transition in three dimensions. This also highlights how nontrivial is the first step of deriving an effective theory for the RFOT phenomenology from a rigorous integration over the short-range fluctuations.

cond-mat.dis-nn↗

arXiv2012

Evidence of growing spatial correlations during the aging of glassy glycerol

We have measured, as a function of the age $t_a$, the aging of the nonlinear dielectric susceptibility $χ_3$ of glycerol below the glass transition. Whereas the linear susceptibility can be accurately accounted for in terms of an age dependent relaxation time $τ_α(t_a)$, this scaling breaks down for $χ_3$, suggesting an increase of the amplitude of $χ_3$. This is a strong indication that the number $N_{corr}$ of molecules involved in relaxation events increases with $t_a$. For $T=0.96 \times T_g$, we find that $N_{corr}$ increases by $\sim 10%$ when $t_a$ varies from $1\mathrm{ks}$ to $100\mathrm{ks}$. This sheds new light on the relation between length scales and time scales in glasses.

cond-mat.soft↗

arXiv2011

Effect of Rare Fluctuations on the Thermalization of Isolated Quantum Systems

We consider the question of thermalization for isolated quantum systems after a sudden parameter change, a so-called quantum quench. In part icular we investigate the pre-requisites for thermalization focusing on the statistical properties of the time-averaged density matrix and o f the expectation values of observables in the final eigenstates. We find that eigenstates, which are rare compared to the typical ones sampled by the micro-canonical distribution, are responsible for the absence of thermalization of some infinite integrable models and play an important role for some non-integrable systems of finite size, such as the Bose-Hubbard model. We stress the importance of finite size effects for the thermalization of isolated quantum systems and discuss two alternative scenarios for thermalization, as well as ways to prune down the correct one.

cond-mat.quant-gas↗

arXiv2010

Do solids flow?

Are solids intrinsically different from liquids? Must a finite stress be applied in order to induce flow? Or, instead, do all solids only look rigid on some finite timescales and eventually flow if an infinitesimal shear stress is applied? Surprisingly, these simple questions are a matter of debate and definite answers are still lacking. Here we show that solidity is only a time-scale dependent notion: equilibrium states of matter that break spontaneously translation invariance, e.g. crystals, flow if even an infinitesimal stress is applied. However, they do so in a way inherently different from ordinary liquids since their viscosity diverges for vanishing shear stress with an essential singularity. We find an ultra-slow decrease of the shear stress as a function of the shear rate, which explains the apparent yield stress identified in rheological flow curves. Furthermore, we suggest that an alternating shear of frequency $ω$ and amplitude $γ$ should lead to a dynamic phase transition line in the ($ω$,$γ$) plane, from a 'flowing' to a 'non-flowing' phase. Finally, we apply our results to crystals, show the corresponding microscopic process leading to flow and discuss possible experimental investigations.

cond-mat.stat-mech↗

arXiv2010

Evidence of growing spatial correlations at the glass transition from nonlinear response experiments

The ac nonlinear dielectric response $χ_3(ω,T)$ of glycerol was measured close to its glass transition temperature $T_g$ to investigate the prediction that supercooled liquids respond in an increasingly non-linear way as the dynamics slows down (as spin-glasses do). We find that $χ_3(ω,T)$ indeed displays several non trivial features. It is peaked as a function of the frequency $ω$ and obeys scaling as a function of $ωτ(T)$, with $τ(T)$ the relaxation time of the liquid. The height of the peak, proportional to the number of dynamically correlated molecules $N_{corr}(T)$, increases as the system becomes glassy, and $χ_3$ decays as a power-law of $ω$ over several decades beyond the peak. These findings confirm the collective nature of the glassy dynamics and provide the first direct estimate of the $T$ dependence of $N_{corr}$.

cond-mat.soft↗

arXiv2010

Super-diffusion around the rigidity transition: Levy and the Lilliputians

By analyzing the displacement statistics of an assembly of horizontally vibrated bidisperse frictional grains in the vicinity of the jamming transition experimentally studied before, we establish that their superdiffusive motion is a genuine Levy flight, but with `jump' size very small compared to the diameter of the grains. The vibration induces a broad distribution of jumps that are random in time, but correlated in space, and that can be interpreted as micro-crack events at all scales. As the volume fraction departs from the critical jamming density, this distribution is truncated at a smaller and smaller jump size, inducing a crossover towards standard diffusive motion at long times. This interpretation contrasts with the idea of temporally persistent, spatially correlated currents and raises new issues regarding the analysis of the dynamics in terms of vibrational modes.

cond-mat.soft↗

arXiv2009

The Random First-Order Transition Theory of Glasses: a critical assessment

The aim of this paper is to summarise the basic arguments and the intuition bolstering the RFOT picture for glasses, based on a finite dimensional extension of mean-field models with an exponentially large number of metastable states. We review the pros and cons that support or undermine the theory, and the directions, both theoretical and experimental, where progress is needed to ascertain the status of RFOT. We elaborate in particular on the notions of mosaic state and point-to-set correlations, and insist on the importance of fluctuations in finite dimensions, that significantly blur the expected cross-over between a Mode-Coupling like regime and the mosaic, activated regime. We discuss in detail the fundamental predictions of RFOT, in particular the possibility to force a small enough system into an ideal glass state, and present several new ones, concerning aging properties or non-linear rheology. Finally, we compare RFOT to other recent theories, including elastic models, Frustration Limited Domains or Kinetically Constrained models.

cond-mat.dis-nn↗

arXiv2009

Evolution of dynamical facilitation approaching the granular glass transition

We investigate the relaxation dynamics of a dense monolayer of bidisperse beads by analyzing the experimental data previously obtained in a fluidized bed. We show that the dynamics is formed by elementary relaxation events called cage jumps. These aggregate on a very short time into clusters. Increasing the packing fraction makes the spatio-temporal organization of the clusters evolve from a rather scattered and random distribution towards a collection of sparse and large events, called avalanches. The avalanche process is a manifestation of dynamical facilitation. The study of its evolution with density reveals that dynamical facilitation becomes less conserved and play a lesser role for the structural relaxation approaching the granular glass transition.

cond-mat.soft↗

arXiv2009

Avalanches and Dynamical Correlations in supercooled liquids

We identify the pattern of microscopic dynamical relaxation for a two dimensional glass forming liquid. On short timescales, bursts of irreversible particle motion, called cage jumps, aggregate into clusters. On larger time scales, clusters aggregate both spatially and temporally into avalanches. This propagation of mobility, or dynamic facilitation, takes place along the soft regions of the systems, which have been identified by computing isoconfigurational Debye-Waller maps. Our results characterize the way in which dynamical heterogeneity evolves in moderately supercooled liquids and reveal that it is astonishingly similar to the one found for dense glassy granular media.

cond-mat.soft↗