Program
- 09.00 Giacomo Gradenigo: Static correlation lengths and domain walls energy in a glass-forming liquid model under confinement.
- 09.40 Smarajit Karmakar: Direct Estimate of the Static Length-Scale Accompanying the Glass Transition.
- 10.20 Corentin Coulais: Jamming at finite temperature: a granular experiment.
- 11.00 Coffee Break
- 11.30 Serena Bradde: The Generalized Arrhenius law in out of equilibrium systems.
- 12.10 Ohzeki Masayuki tba
- 12.50 Lunch time
- 14.00 Maria Chiara Angelini: Ensemble renormalization group for disordered systems.
- 14.40 Pierfrancesco Urbani: Critical slowing down exponents in the theory of the replicated liquid.
- 15.20 Khanh-dang Nguyen Thu Lam: Selection in glassy and two-states dynamics
- 16.00 Coffee Break
- 16.30 Victor Bapst on the quantum annealing of quantum mean-field models.
- 17.10 Ana Carolina Ribeiro Texeira on ergodicity properties of the anderson model on the bethe lattice
- 17.50 End
Abstracts
Giacomo GRADENIGO: Static correlation lengths and domain walls energy in a glass-forming liquid model under confinement.
We study by means of numerical simulations the thermodynamics of a glass forming liquid confined within a "sandwich" geometry, namely between two rough walls made of particles frozen in their equilibrium positions in a low temperature glassy state of the liquid.
We individuate and measure two characteristic lengths: the point-to-set length, which is typical of the random first-order theory, and the penetration length. The two lengths show a remarkable different behavior when the temperature is lowered. We also study the thermodynamics of the sandwich cavity when it is pinned at the borders with different amorphous states: when the distance between the amorphous boundaries is small enough we are able to measure the energy cost of the domain wall induced by such heterogeneous boundary conditions.
Smarajit KARMAKAR: Direct Estimate of the Static Length-Scale Accompanying the Glass Transition.
Glasses are liquids whose viscosity has increased so much that they cannot flow. Accordingly there have been many attempts to define a static length-scale associated with the dramatic slowing down of super-cooled liquid with decreasing temperature. In this talk, I will present a simple method to extract the desired length-scale which is highly accessible both for experiments and for numerical simulations. The fundamental new idea is that low lying vibrational frequencies come in two types, those related to elastic response and those determined by plastic instabilities. The minimal observed frequency is determined by one or the other, crossing at a typical length-scale which is growing with the approach of the glass transition. This length-scale characterizes the correlated disorder in the system: on longer length-scales the details of the disorder become irrelevant, dominated by the Debye model of elastic modes. After introducing the length-scale I will show how this scale completely determines the dynamics of the super-cooled liquid under external constraints, thereby proving beyond doubt the static nature of the proposed length-scale. Finally I talk about consequence of this scale on the mechanical properties of the amorphous solids.
Corentin COULAIS: Jamming at finite temperature: a granular experiment.
We study experimentally the vicinity of the Jamming transition by investigating the statics and the dynamics of the contact network of an horizontally shaken bi-disperse packing of photo-elastic disks. Compressing the packing very slowly, while maintaining a mechanical excitation, we produce a granular glass, namely a frozen structure of vibrating grains.
The contact network of this glass phase exhibits a remarkable "glassy" behavior. First, the average number of contacts displays a abrupt variation that also corresponds to the packing fraction at which the contact network relaxation time diverges. At a distinct and smaller packing fraction, we observe strong maximum dynamical heterogeneities of the contact network, signing in turn a dynamical crossover. We further discuss the link between the "dynamical transition" and spatial correlations and the interplay of the two crossovers with the zero temperature jamming transition of frictionless soft spheres.
Serena BRADDE: The Generalized Arrhenius law in out of equilibrium systems.
The Arrhenius law appears in many different contexts. It is one of the most important laws governing the physics of systems at equilibrium characterized by energy scales much larger than the temperature. However, as we shall show, it is more general and it can be extended also in systems that are out of equilibrium either because are subjected to non-potential forces or are coupled to an out of equilibrium thermal bath. In the equilibrium case, the validity of the Arrhenius law is traced back to the existence of time reversal symmetry. In the out-of-equilibrium regime the same connection holds with a generalization of time-reversal discovered in the context of fluctuation theorems.
Ohzeki MASAYUKI
TBA
Maria Chiara ANGELINI: Ensemble Renormalization Group for Disordered Systems.
We study a Renormalization Group transformation that can be used also for models with quenched disorder, like spin glasses. The method is based on a mapping between disorder distributions, chosen such as to keep some physical properties (e.g. the ratio of correlations) invariant under the transformation. We validate this Ensemble Renormalization Group by applying it to the hierarchical model (both the diluted ferromagnetic version and the spin glass version), finding results in agreement with Monte Carlo simulations.
Pierfrancesco URBANI: Critical slowing down exponents in the theory of the replicated liquid.
The mode coupling exponent parameter lambda is a dynamical quantity which describes how the correlation function behaves near the plateau when the dynamical transition is approached. It is of interest also because it can be connected to the alpha relaxation time. However, even if it is a purely dynamical quantity, Caltagirone et. al. showed that in schematic MCT models it can be derived from the static replicated Gibbs free energy. Here we want to extend this result in the framework of the theory of the replicated liquid that was investigated by Mézard and Parisi. We will derive an explicit expression for this exponent using the HNC approximation.
Khanh-Dang NGUYEN THU LAM: Selection in glassy and two-states dynamics.
We study a population of systems evolving with the same dynamics. Each system in this population can give birth to a clone of itself or disappear, with a probability rate that depends on its position in the phase space of the dynamics. Such population dynamics are related to a broad range of processes, including natural selection in populations of living species, reaction-diffusion models, cloning algorithms used to simulate large deviations. We focus on the case of a population evolving in a glassy energy landscape and the elementary version of it: the case of a two-state system, which is interesting as soon as selection comes into play.
Victor BAPST: On the Quantum Annealing of Quantum Mean-Field Models.
In this talk I will present results obtained on fully-connected mean-field models of quantum spins with p-body ferromagnetic interactions and a transverse field, as a toy model for studying quantum annealing of disordered systems. For p=2 this corresponds to the quantum Curie-Weiss model which exhibits a second-order phase transition, while for p>2 the transition is first order. We provide a refined analytical description of both the static and dynamics properties of these models, allowing us to study the slow annealing from the pure transverse field to the pure ferromagnet (and vice versa) and discuss the effect of first-order phase transition and spinodals on the residual excitation energy, both on finite and exponentially divergent time-scales. We expect the general features that we found to be relevent for real disordered optimization problems.
Ana Carolina RIBEIRO-TEXEIRA: Ergodicity properties of the Anderson model on the Bethe lattice.
I will present some results on an ongoing work on the ergodicity properties of the Anderson model defined on the Bethe lattice. Our study is motivated by the conjectured existence of a phase for intermediary disorder strength values whose ergodicity properties are distinct from the fully ergodic extended phase, as well as from the completely ergodicity broken localised one. Apart from the intrinsic interest in studying these different ergodicity regimes, the relevance of this investigation also bares on the relation of the aforementioned model to the many-body localization problem, through a mapping of the decay of quasi-particle states of the interacting system in Fock space representation onto an appropriate Anderson (single-particle) localisation problem on a tree. For an ensemble of system's realizations, we have studied eigenvalues and eigenstates statistics through exact diagonalization. In particular we analysed the neighboring gaps ratio statistics, the statistics of inverse participation ratios, including multifractality analysis. We find evidence of the presence of an intermediary disorder phase whose corresponding statistics are neither expressing extended nor localised states.
