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Abstracts

Ludovic Berthier (Universite de Montpellier II)

Title: Thermodynamic fluctuations in spin and atomic models of supercooled liquids
Abstract: Theoretical approaches to the physics of glass-forming materials can be broadly organized in two categories, putting forward either a static (configurational entropy, geometrical motifs) or a dynamic (defects, dynamic facilitation) viewpoint. I will present results from computer simulations showing that viscous liquids approaching the glass transition develop non-trivial thermodynamic fluctuations which strongly correlate with the emergence of slow dynamics. A direct consequence of these findings is the possibility to induce equilibrium phase transitions by applying external fields to supercooled liquids. I will present numerical results supporting the existence of two such transitions, and compare the results with the ones obtained in a bi-dimensional spin plaquette model.

Oriane Blondel (Paris 7)
Title: Front progression in the East model
Abstract: The East model is a celebrated toy model for glassy dynamics. It is a one-dimensional, non-attractive interacting particle system with Glauber dynamics, in which a flip is prohibited at a site x if the right neighbour x+1 is inactive. Starting from a configuration entirely inactive on the left half-line, we prove a law of large numbers for the position of the left-most zero (the front), as well as ergodicity of the process seen from the front. For want of attractiveness, this one-dimensional shape theorem cannot be derived by the usual coupling arguments but relies instead on quantifying the local relaxation to the non-equilibrium invariant measure for the process seen from the front. We also briefly discuss more recent results by Ganguly, Lubetsky and Martinelli showing normal fluctuations for the front.

Alessandra Faggionato (La Sapienza)
Title: East-like processes
Abstract: Following the survey of F. Martinelli, we focus on some special issues of the East process and its higher dimensional versions. In particular, we investigate the low-temperature asymptotics of relaxation times (in finite/infinite volume) and the spreading of vacancies (i.e. mobile domains) generated by a frozen one. As a byproduct of a renormalization group analysis and potential theory for resistor networks, we derive tight bounds on the relaxation times and vacancy hitting times related to time-scale separation, dynamical hetereogeneity and the geometry of vacancy waves. Joint work with P. Chleboun and F. Martinelli.

Juan P. Garrahan (Nottingham)
Title: Kinetically constrained models, from classical to quantum
Abstract: TBA

Robert Jack (Bath)
Title: Metastable states and their consequences, in kinetically constrained models and plaquette spin systems
Abstract: In describing glassy phenomena, one often thinks of metastable states, separated by free energy barriers. In kinetically constrained models, it is not trivial to define metastable states: we show how this can be done in the East model [1] using a recent dynamical construction due to Kurchan and Levine [2]. Building on these ideas, we discuss how plaquette spin models respond to random pinning [3] and to coupling between different replicas [4].
[1] R. L. Jack, Phys. Rev E 88, 062113 (2013).
[2] J. Kurchan and D. Levine, J. Phys. A 44, 035001 (2011).
[3] R. L. Jack and L. Berthier, Phys. Rev. E 85, 021120 (2012).
[4] J. P. Garrahan, Phys. Rev. E 89, 030301(R) (2014).

Vivien Lecomte (Paris VII)
Title: Finite-size effects for the dynamical phase coexistence in a mean-field kinetically constrained model
Abstract: On the example of a mean-field Fredrickson-Andersen kinetically constrained model, we focus on the known property that equilibrium dynamics takes place at a first-order dynamical phase transition point in the space of time-realizations. We investigate the finite-size properties of this first order transition. By discussing and exploiting a mapping of the classical dynamical transition – an argued signature of dynamical heterogeneities – to a first-order quantum transition, we show that the quantum analogy can be exploited to extract finite-size properties. Results shed light on anomalous features of distributions of history-dependent observables in models of glasses.

Arturo Leos Zamorategui (Paris VII)
Title: Anomalous scaling in the glassy dynamics of the Fredrickson-Andersen model in 1+1 dimensions
Abstract: Kinetically Constrained Models (KCMs) are toy models for glassy dynamics whose static features can be very simple, while dynamical features present hysteresis, aging and slow relaxation – non-trivial features characteristic of glassy phenomena. The steady state of many of those glass formers is characterized by a coexistence between active and inactive dynamical phases, which can be described by a first-order (dynamical) phase transition. I focus on the active and inactive regions of the Friedrickson-Andersen model in a unidimensional discrete lattice with continuous time dynamics. In such a model particles represent active and inactive coarse-grained regions of a glass: changes in the configuration occur in the vicinity of active region. By extensive numerical simulations I analyze the regions of inactivity and the nature of their interactions (in space-time) whose boundaries are random walks that branch and coalesce. One investigates how anomalous scaling exponents can arise due to such interactions. In order to describe the dynamics of this model we propose an effective model, also offering a tool to understand a broader class of KCMs.

Fabio Martinelli (Roma Tre)
Title: East model: mixing time, cutoff and dynamical heterogeneities
Abstract: The East model is a linear chain of spins, each labeled either 0 or 1, evolving according to a very simple rule:
i) with rate one and independently for each vertex, a new value 1/0 is proposed with probability 1-q and q respectively;
ii) the proposed value is accepted iff the spin immediately to the left is labeled "0".
The above is just an example of a general class of interacting particle systems in which the local update of a spin occurs only in the presence of a special ("facilitating") configuration at neighboring vertices. Although the i.i.d. Bernoulli(1-q) distribution remains a reversible stationary measure, the relaxation to equilibrium of these chains can be extremely complex, featuring dynamical phase transitions, metastability, dynamical heterogeneities and universal behavior. The East model and its generalizations play an important role as models for the dynamics of real glasses, where small values of q correspond to low temperatures.
After the pioneering work by Aldous and Diaconis in 2001 on the relaxation time of the process, several further mathematical progresses have been achieved which improved and sometimes correct quite basic assumptions made by the physicists. In this talk I will survey some of the most relevant ones.

Mike Moore (Manchester)
Title: Glasses and Jamming: lessons from hard disks in a narrow channel
Abstract: The thermodynamic properties of disks moving in a channel sufficiently narrow that they can only collide with their nearest neighbours can be solved exactly by determining the eigenvalues and eigenvectors of an integral equation. Using it we have determined the correlation length ξ of this system. We have developed an approximate solution which becomes exact in the high density limit. It describes the system in terms of defects in the zigzag arrangement of disks found in the high-density limit. The correlation length is then effectively the spacing between the defects. The time scales for defect creation and annihilation are determined with the help of transition state theory as is the diffusion coefficient of the defects and they are in good agreement with molecular dynamics simulations. On compressing the system with the Lubachevsky-Stillinger procedure jammed states are obtained whose φJ are a function of the compression rate γ. We can quantitatively explain this dependence by using the Kibble-Zurek hypothesis. We have also determined the point-to-set length scale for this system and it is much smaller than ξ with a completely different dependence on the packing fraction.
The case of wider channels in which the disks can interact with their next-nearest neighbours can also be studied by similar methods. It has features not seen in the nearest-neighbour case, but which seem to be present in three dimensional jammed states of hard spheres.

Takahiro Nemoto (Kyoto)
Title: Computation of Large Deviation Statistics via Iterative Measurement-and-Feedback Procedure
Abstract: KCMs show the dynamical phase transition when they are biased with respect to the activity of the system, where the biased measure is defined by multiplying an exponential function to the original path measure. The normalisation constant of the measure leads to the definition of a dynamical free energy, which echoes the formula that thermodynamic free energy is calculated by the logarithm of the partition function. The dynamical free energy shows a singularity as if equilibrium thermodynamic free energy has a singularity in equilibrium phase transition.
In equilibrium thermodynamics, free energy is constructed with an operational manner, meaning that observable quantities of the system, say volume as a function of the pressure and temperature for example, is used for calculating thermodynamic free energy. This operational construction may help us to understand the singularity of the thermodynamic function. For example, we know that the equation of state has two brunches at the 1st order transition point creating the singularity in the thermodynamic free energy.
Now, we will ask if we can understand the dynamical phase transition in an operational viewpoint. For this, we study how to construct dynamical free energy in an operational manner. We introduce a method, which was invented recently by us for obtaining the dynamical free energy, where only an operational manner was used [1]. Then, we apply it to 1d-FA model and try to depict the operational nature of the dynamical phase transition.
[1]T. Nemoto and S. Sasa, Phys. Rev. Lett. 112, 090602 (2014)

Peter Sollich (King's College London)
Title: Large deviations of the dynamical activity in the East model: analysing structure in biased trajectories
Abstract: We consider large deviations of the dynamical activity in the East model. We bias this system to larger than average activity and investigate the structure that emerges. To best characterise this structure, we exploit the fact that there are effective interactions that would reproduce the same behaviour in an equilibrium system. We combine numerical results with linear response theory and variational estimates of these effective interactions, giving the first insights into such interactions in a many-body system, across a wide range of biases. The system exhibits a hierarchy of responses to the bias, remaining quasi-equilibrated on short length scales, but deviating far from equilibrium on large length scales. We discuss the connection between this hierarchy and the hierarchical aging behaviour of the system. Joint work with Robert L. Jack.

Gilles Tarjus (Paris VI)
Title: Effective theories of the glass transition: thermodynamic versus dynamic approaches
Abstract: TBA

Frédéric van Wijland (Paris 7)
Title: Comparing two dynamics with the same energy landscape
Abstract: We consider a system of pairwise interacting particles performing Brownian motion. The density modes of this system evolve according to the so-called Dean-Kawasaki equation. Their correlations -the dynamic structure factor- have been argued to exhibit slowing down at low temperature, when entering the supercooled regime.
We choose to postulate alternative dynamics for the density modes that however sample the very same equilibrium distribution as the previous dynamics. While being largely fictitious and artificial, these fulfill basic physical requirements like local particle conservation and detailed-balance. We will then argue that no glassiness can emerge from these alternative dynamics, irrespective of the energy landscape density modes live in.
Work done in collaboration with Hugo Jacquin, Bongsoo Kim and Kyozi Kawasaki.