Simons Collaboration on Cracking the Glass Problem Annual Meeting 2022
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Date & Time
Organizer:
Sidney Nagel, University of Chicago
Meeting Goals:
The sixth annual meeting of the collaboration will highlight the progress that has been made in pursuing the original, stated goals of the Simons Collaboration on Cracking the Glass Problem, the main goal of which is to develop a complete and quantitative description of the glass transition, connecting the explicit and quantitative mean-field and zero-temperature theories that have been developed.
The aim to create a predictive theory of glasses, including dynamics, in finite dimension at finite temperatures has provided a new vision for this branch of statistical and mathematical physics. As was made apparent by the award of this year’s Nobel Prize to collaboration member Giorgio Parisi, this work has implications for a wide range of systems. The tools developed by creating such a framework are having important ramifications for a broad range of fields. The annual meeting will explore new connections between the many fields of research that are involved with glassy and amorphous problems.
Speakers:
Carolina Brito, Universidade Federal do Rio Grande do Sul
Eric Corwin, University of Oregon
Leticia Cugliandolo, Université Pierre et Marie Curie – Paris VI
Emanuela Del Gado, Georgetown University
Silvio Franz, Université Paris-Sud
David Huse, Princeton University
Valentina Ros, CNRS and Université Paris Saclay
Thomas Witten, University of Chicago
Carolina Brito
Universidade Federal do Rio Grande do Sul
Jamming with Extra Degrees of Freedom and Tunable Roughness View Slides (PDF)
Although the jamming transition has been extensively studied, there are open questions mainly in the generic situation of nonspherical particles or in presence of friction. While isostaticity is ensured in the case of the jamming of spherical and frictionless particles, nonspherical particles are hypostatic at jamming and frictional spherical particles seem to be hyperstatic at jamming. The presence of asphericity affects, for example, the critical exponents related to the contact number and the vibrational density of states. In this talk Carolina Brito will present some advances in the understanding of the scaling properties of the nonspherical particles at the jamming point and a model where friction can be explored by tuning particles’ roughness, enabling an interpolation from a situation where a system is hyperstatic to a situation where it is hypostatic.
The concept of an ideal glass is seemingly absurd: How can an amorphous structure possibly have the same entropy as the crystal? And yet, if the glass transition is indeed a thermodynamic transition, then the ideal glass must exist as the endpoint of this transition. Here, Eric Corwin and his team show how one can sidestep the limitations of thermal relaxation to obtain the amorphous ground state of polydisperse 2D disk packings. By exploiting additional degrees of freedom — in like fashion to the swap — breathing and free-then-freeze algorithms, we are able to construct packings with all of the hallmarks of the zero-temperature limit of an ideal glass. These packings are 1) critically jammed, 2) ultra-stable, 3) Delaunay triangulated (i.e., every nearest neighbor is also a contacting neighbor), 4) fully saturated, 5) rattler free, 6) hyper-uniform and 7) have a packing fraction that is denser than that of a size-segregated crystalline packing. Corwin will discuss the implications of these structures as well as why this particular construction is only possible in two dimensions.
Leticia Cugliandolo
École Normale Supérieure de Paris
Leticia Cugliandolo will discuss several intriguing aspects of the motility-induced phase separation (MIPS) between a dense and a dilute phase in active Brownian particles in two dimensions. Some of these are the following: the growth of the dense phase follows a law akin to the one of liquid-gas phase separation, which could also be described with a Smoluchowski cluster aggregation picture. During the growth period, the individual clusters can be identified and followed, and effective dynamic equations for their motion proposed. The dense clusters are made of a mosaic of hexatic microdomains whose sizes do not coarsen indefinitely, leaving behind a network of extended topological defects from which microscopic dilute bubbles arise, help the clusters displace and later heal.
Emanuela Del Gado
Georgetown University
Elasticity, Rigidity and Rheology of Soft Particulate Gels View Slides (PDF)
Many materials we eat, spread, squeeze, or 3D print are gels — soft, amorphous solids whose solid component is constituted by a network of self-assembled particles or agglomerated smaller units (proteins, polymers or other particulates). The understanding of the emergence of rigidity and of the role of stress localization in the mechanics of this type of gels has just started, but it is clearly key to designing and expanding their performances and functions. Emanuela Del Gado will discuss new insight into the fundamental physics that control rigidity, elasticity and rheology of soft particulate gels. Mechanical heterogeneities, often not recognizable from structures and morphologies, translate into stress and strain localization when the material is deformed or under load. The outstanding questions are whether there exist organizing principles in the gel microstructures that can encompass different compositions and gelation processes and whether it is possible to identify common underlying mechanisms in the rheological response.
Silvio Franz
Laboratoire de Physique Théorique et Modèles Statistiques Universite Paris-Sud
The soft modes of spin glasses have been studied for a long time. Still a field theory of fluctuations is not accomplished both in equilibrium and in dynamics. In this talk Silvio Franz will discuss a theory of space fluctuations in spin glasses in equilibrium based on the method of effective potential, which is flat in the low-temperature phase. He will discuss the relation of the effective potential flatness with the vanishing of ‘replicon’ eigenvalues of the small fluctuation matrix and provide a convenient physical basis to study fluctuations. Franz will show how the construction of a sigma model of these fluctuations leads to a nonstandard field theory with a nonanalytic dependence in the gradient of the fluctuating field.
Many-body localization (MBL) is the failure of a generic, closed, interacting many-body quantum system to act as a ‘bath’ for its subsystems and bring itself to thermal equilibrium under its own unitary quantum dynamics. There are two regimes of many-body localization: (1) a true many-body localized (MBL) phase, where the MBL is stable in the limit of infinite systems and infinite time; and (2) a transient MBL regime, where, like in some structural glasses, the freezing lasts for extremely long times but is expected not to persist to the infinite time limit. David Huse will review some aspects of our current understanding of these glassy phenomena.
Valentina Ros
CNRS and Université Paris Saclay
Geometrical Properties of High-d Non-Convex Landscapes View Slides (PDF)
In this talk, Valentina Ros will present some work done within the collaboration concerning the geometrical properties (mainly, the distribution and connectivity of stationary points) of random nonconvex landscapes in high dimension. Random landscapes with Gaussian statistics have been introduced long ago as toy models of complex potential landscapes of glassy systems; understanding their structure has been (and is) instrumental for determining the evolution of local dynamics of the associated glassy systems. In more recent years, these landscapes made their appearance as generalized cost functions in a variety of high-dimensional optimization, inference and control problems. In the talk, Ros will comment on the analytical methods available to compute the statistics of stationary points and discuss applications to (1) the problem of barrier crossing in large-but-finite fully connected models, (2) a problem of denoising of tensors in high dimension and (3) a complex dynamical system modeling well-mixed ecosystems with asymmetric interactions.
Thomas Witten
University of Chicago
Entrapment into Order, a Fate of Discrete, Deterministic Dynamics View Slides (PDF)
Cyclic annealing in a jammed particle system as studied numerically, for example, by Sastry et al. and by Lavrentovitch Liu and Nagel, exhibits a peculiar form of ordering. Imposing repeated quasistatic cycles of forward and reverse shear displacements results in a gradual evolution of the motion from disorderly relaxation events to an exactly repeating sequence of locally stable microstates. The repeat period may be a single annealing cycle or a multiple of it, showing subperiodic behavior. Increasing shear amplitude leads to longer subharmonics, terminating in a breakdown of the ordering process.
Two simple features of this system account generally for the ordering process. Configurations are discrete and deterministic. Thus the dynamics are a discrete mapping on the set of configurations. This talk explores the effect of incorporating one further effect observed in annealing. The individual transitions composing the map are local, involving only a few degrees of freedom at a particular location in the system. In this talk, Witten will explore maps between configurations involving such small regions of space. The local behavior of annealing events means that the map connects only configurations that are nearby in space, within a particular ‘step length.’ He will create arbitrary local maps on configuration sets with 1,000 points placed randomly in a square. Small step lengths lead to rapid trapping at final point or loop close to the starting point. As the step length increases, the distance spanned during convergence grows to the size of the system. Witten compares this model transition with the observed breakdown of ordering in annealed packs.
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