Related papers: Phase space geometry and slow dynamics
The short- and long-time dynamics of model systems undergoing a glass transition with apparent inversion of Kauzmann and dynamical arrest glass transition lines is investigated. These models belong to the class of the spherical mean-field…
We study dynamical aspects of three--dimensional gonihedric spins by using Monte--Carlo methods. The interest of this family of models (parametrized by one self-avoidance parameter $\kappa$) lies in their capability to show remarkably slow…
A mean-field model of Ising spin glass with the Hamiltonian being a sum of the infinite-range ferromagnetic and random antiferromagnetic interactions is studied. It is shown that this model has phase transition in external magnetic field…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
The nonexponential relaxation ocurring in complex dynamics manifested in a wide variety of systems is analyzed through a simple model of diffusion in phase space. It is found that the inability of the system to find its equilibrium state in…
The weak ergodicity breaking hypothesis postulates that out-of-equilibrium glassy systems lose memory of their initial state despite being unable to reach an equilibrium stationary state. It is a milestone of glass physics, and has provided…
Observations of glassy dynamics in experiments on confluent cellular tissue have inspired a wealth of computational and theoretical research to model their emergent collective behavior. Initial studies of the physical properties of several…
In these four lectures I describe basic ideas and methods applicable to both classical and quantum systems displaying slow relaxation and non-equilibrium dynamics. The first half of these notes considers classical systems, and the second…
High dimensional dynamics play a vital role in brain function, ecological systems, and neuro-inspired machine learning. Where and how these dynamics are confined in the phase space remains challenging to solve. Here, we provide an analytic…
In order to understand the mechanisms for glassy dynamics in biological tissues and shed light on those in non-biological materials, we study the low-temperature disordered phase of 2D vertex-like models. Recently it has been noted that…
In this paper we study the out-of-equilibrium phase diagram of the quantum version of Derrida's Random Energy Model, which is the simplest model of mean-field spin glasses. We interpret its corresponding quantum dynamics in Fock space as a…
The glass transition, extensively studied in dense fluids, polymers, or colloids, corresponds to a dramatic evolution of equilibrium transport coefficients upon a modest change of control parameter, like temperature or pressure. A similar…
We investigate the non-equilibrium dynamics of spherical spin models with two-spin interactions. For the exactly solvable models of the d-dimensional spherical ferromagnet and the spherical Sherrington-Kirkpatrick model the asymptotic…
Among the key insights into the glass transition has been the identification of a non-equilibrium phase transition in trajectory space which reveals phase coexistence between the normal supercooled liquid (active phase) and a glassy state…
We review an scenario for the non-equilibrium dynamics of glassy systems that has been motivated by the exact solution of simple models. This approach allows one to set on firmer grounds well-known phenomenological theories. The old ideas…
The dynamics of glass formation in monatomic and binary liquids are studied numerically using a microscopic field theory for the evolution of the time-averaged atomic number density. A stochastic framework combining phase field crystal free…
We study the off-equilibrium relaxational dynamics of the Amit-Roginsky $\phi^3$ field theory, for which the mode coupling approximation is exact. We show that complex phenomena such as aging and ergodicity breaking are present at low…
Slow conductance relaxations are observable in a many condensed matter systems. These are sometimes described as manifestations of a glassy phase. The underlying mechanisms responsible for the slow dynamics are often due to structural…
The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher…
Glassy systems are disordered systems characterized by extremely slow dynamics. Examples are supercooled liquids, whose dynamics slow down under cooling. The specific pattern of slowing-down depends on the material considered. This…