Session C44: Dynamics in Glassy Systems

Connections between classical mean field models with glassy dynamics and quantum SYK models

TBD   

On the trap model description of glassy dynamics

The description of activated dynamics of glassy systems in the multidimensional configurational space is a long-standing open problem. In this talk I will discuss about recent studies of the equilibrium and out-of equilibrium dynamics of a number of models with rough potential energy landscapes. These models provide examples of dynamics where typical relaxation channels go over finite potential energy barriers despite the presence of less-energy-demanding escaping paths in configurational space. This phenomenon is naturally expected to be relevant in the thermally activated regime of realistic models of glass-formers. The numerical and analytic results will show whether, and to what extent, due to this phenomenon the activated dynamics displayed by these models can be effectively described in terms of the fully solvable dynamics of thermally-activated systems like trap models.   

Statistical properties of barriers and activated dynamics in mean-field models of glasses

Understanding the geometrical properties of high-dimensional, random energy landscapes is a central problem in the physics of glassy systems, as well as in interdisciplinary applications to computer science, ecology and biology.
In this talk I will discuss a framework to compute the statistical distribution of stationary points of random landscapes, making use of a replicated version of the Kac-Rice formula. I will focus on models which provide a mean-field description of the glass transition, and discuss how to compute the statistics of the energy barriers between local minima of the landscape. I will discuss the dynamical implications on these results, especially for the activated regime of the dynamics.   

Glassy dynamics: mean-field theory and beyond

The slowing down of a liquid's dynamics upon approaching the glass transition is accompanied by a number of novel dynamical phenomena: transient localization of particles' positions, strong spatial and temporal fluctuations of the dynamics of individual particles, etc. The description of these dynamics, even at the level of a mean-field theory, is still being developed. I will present a simple theory for the dynamics of mean-field-like models of glass forming liquids. Next, I will turn to the glassy dynamics of one particle moving in a frozen matrix and, in this simpler case, show how one can incorporate dynamic events neglected in the mean-field approach.   

New computational approaches to dynamics in complex landscapes

TBD