Related papers: Time Glass: A Fractional Calculus Approach
Glass forming liquids exhibit a rich phenomenology upon confinement. This is often related to the effects arising from wall-fluid interactions. Here we focus on the interesting limit where the separation of the confining walls becomes of…
Glasses are out-of-equilibrium systems aging under the crystallization threat. During ordinary glass formation, the atomic diffusion slows down rendering its experimental investigation impractically long, to the extent that a timescale…
We propose a connection between self-similar, focusing dynamics in nonlinear partial differential equations (PDEs) and macroscopic dynamic features of the glass transition. In particular, we explore the divergence of the appropriate…
The Shapere-Wilczek model \cite{wil}, or so called $ fgh$ model, enjoys the remarkable features of a Time Crystal (TC) that has a non-trivial time dependence in its lowest energy state (or the classical ground state). We construct a…
In ref. cond-mat/0005372, Sastry studies by numerical simulations the phase diagram of a simple fragile glass-forming liquid, presenting very interesting and clear results. We apply to this system, at various density values, the analytic…
A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle,…
The notion of spontaneous symmetry breaking has been well established to characterize classical and quantum phase transitions of matter, such as in condensation, crystallization or quantum magnetism. Generalizations of this paradigm to the…
In the past few years, the theory of thermal transport in amorphous solids has been substantially extended beyond the Allen-Feldman model. The resulting formulation, based on the Green-Kubo linear response or the Wigner-transport equation,…
This paper is an extended version of an article accepted for publication in Physical Review E. Besides its fundamental interest, the model that we investigate in this article is simple enough to be used as a basis for courses or tutorials…
We propose a scenario for the glass transition based on the cooperative nature of nucleation processes and entropic effects. The main point is the relation between the off-equilibrium energy dissipation and nucleation processes in…
In this talk I will show that usual spin glasses are a peculiar kind of Abelian gauge theory. I will shortly review the techniques used to study them. At the end I will consider more general models (e.g. spin glasses based on non Abelian…
In the context of a classical example of glass-formation in 3-dimensions we exemplify how to construct a statistical mechanical theory of the glass transition. At the heart of the approach is a simple criterion for verifying a proper choice…
Dynamical heterogeneities -- strong fluctuations near the glass transition -- are believed to be crucial to explain much of the glass transition phenomenology. One possible hypothesis for their origin is that they emerge from soft…
We investigate the liquid-glass phase transition in a system of point-like particles interacting via a finite-range attractive potential in D-dimensional space. The phase transition is driven by an `entropy crisis' where the available phase…
The problems of the intermediate-range atomic structure of glasses and of the mechanism for the glass transition are approached from the low-temperature end in terms of a scenario for the atomic organization that justifies the use of an…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
We summarize a theoretical framework based on global time-reparametrization invariance that explains the origin of dynamic fluctuations in glassy systems. We introduce the main ideas without getting into much technical details. We describe…
A lattice model of spinless interacting electrons is used to formulate the Landau theory of the Fermi liquid to electron glass quantum phase transition. We demonstrate that the presence of additional random site energies does not affect the…
We discuss the slow, nonequilibrium, dynamics of spin glasses in their glassy phase. We briefly review the present theoretical understanding of the spectacular phenomena observed in experiments and describe new numerical results obtained in…
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…