Related papers: Time Glass: A Fractional Calculus Approach
The topic of the glass transition gives rise to a a wide diversity of views. It is, accordingly, characterized by a lack of agreement on which would be the most profitable theoretical perspective. In this chapter, I provide some elements…
The excitation-chain theory of the glass transition, proposed in an earlier publication, predicts diverging, super-Arrhenius relaxation times and, {\it via} a similarly diverging length scale, suggests a way of understanding the relations…
We provide a theoretical perspective on the glass transition in molecular liquids at thermal equilibrium, on the spatially heterogeneous and aging dynamics of disordered materials, and on the rheology of soft glassy materials. We start with…
We propose a microscopic model without energy barriers in order to explain some generic features observed in structural glasses. The statics can be exactly solved while the dynamics has been clarified using Monte Carlo calculations.…
Dense liquids gradually transform into non-equilibrium amorphous solids as they pass through the experimental glass transition. Experimentally, ergodicity is lost because measurements are conducted within a finite time window. More than…
Investigation of states with a periodic time dependence of physical quantities attracts a considerable interest now. Although it has been proposed initially that such states (coined Quantum Time Crystals) might be macroscopic and…
A picture for thermodynamics of the glassy state was introduced recently by us (Phys. Rev. Lett. {\bf 79} (1997) 1317; {\bf 80} (1998) 5580). It starts by assuming that one extra parameter, the effective temperature, is needed to describe…
Time crystals are quantum many-body systems which, due to interactions between particles, are able to spontaneously self-organize their motion in a periodic way in time by analogy with the formation of crystalline structures in space in…
Based on experimental evidences we present a phenomenological description of the thermal glass transition as a dynamical phase transition. Different susceptibilities calculated on the basis of this description are in good qualitative…
The analytical model of a glass-forming system is formulated within the formalism analogous to gauge theory constructions in quantum field theory. This work explores the scope of the proposed approach and investigates the equilibrium…
Glass formation is one of the most interesting phenomena in the condensed matter field. Considerable effort has gone into understanding and predicting the glass formability. However, the previous prediction requires the glass first made…
Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order,…
This is a short account of the basic principles of a comprehensive theory of the vitreous state, looking at glasses and their eventual <<melting>> into a liquid state (the inverse glass <<transition>>) from the perspective of their…
We generalize the simplest kinetically constrained model of a glass-forming liquid by softening kinetic constraints, allowing them to be violated with a small finite rate. We demonstrate that this model supports a first-order dynamical…
We show the existence of intermittent dynamics in one of the simplest model of a glassy system: the two-state model, which has been used to explain the origin of the violation of the fluctuation-dissipation theorem. The dynamics is analyzed…
Topological defects are typically quantified relative to ordered backgrounds. The importance of these defects to the understanding of physical phenomena including diverse equilibrium melting transitions from low temperature ordered to…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
This Ph.D. thesis is divided in two parts. The first one concerns the equilibrium properties of glassy systems. Some aspects of the phenomenology of glasses and of theories attempting to describe them are reviewed in chapter 1. A study of…
We describe a model for the colloidal glass transition that is based on Feynman's theory for the $\lambda$-transition in liquid helium. Our model essentially counts the number of configurations of dynamic loops, strings or clusters of…
In the mode coupling theory of the liquid to glass transition the long time structural relaxation follows from equations solely determined by equilibrium structural parameters. The present extension of these structural relaxation equations…