Related papers: Escaping from cycles through a glass transition
When confined to a topological environment consisting of a cycle coupled with a half-line, quantum walks exhibit long-term statistical tendencies which differ dramatically from the tendencies of classical random walks in the same…
We obtain analytic expressions for the time correlation functions of a liquid of spherical particles, exact in the limit of high dimensions $d$. The derivation is long but straightforward: a dynamic virial expansion for which only the first…
The nature of the glass transition is theoretically understood in the mean-field limit of infinite spatial dimensions, but the problem remains totally open in physical dimensions. Nontrivial finite-dimensional fluctuations are hard to…
We study Markov chains on a lattice in a codimension-one stratified independent random environment, exploiting results established in [2]. First of all the random walk is transient in dimension at least three. Focusing on dimension two,…
Stochastic systems characterised by a random driving in a form of the general stable noise are considered. The particle experiences long rests due to the traps the density of which is position-dependent and obeys a power-law form attributed…
We introduce a three-dimensional lattice gas model to study the glass transition. In this model the interactions come from the excluded volume and particles have five arms with an asymmetrical shape, which results in geometric frustration…
We introduce a lattice model of glass transition in polymer globules. This model exhibits a novel scenario of ergodicity breaking in which the disjoint regions of phase space do not arise uniformly, but as small chambers whose number…
We introduce a general class of random walks on the $N$-hypercube, study cut-off for the mixing time, and provide several types of representation for the transition probabilities. We observe that for a sub-class of these processes with long…
We use computer simulations to investigate the static properties of a simple glass-forming fluid in which the positions of a finite fraction of the particles has been frozen in. By probing the equilibrium distribution of the overlap between…
One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass…
We study random walks evolving in continuous time on a one-dimensional lattice where each site $x$ hosts a quenched random potential $U_x$. The potentials on different sites are independent, identically distributed Gaussian random…
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…
We study nearest-neighbors branching random walks started from a point at the interior of a hypercube. We show that the probability that the process escapes the hypercube is monotonically decreasing with respect to the distance of its…
We formulate and solve a model of dynamical arrest in colloids. A particle is coupled to the bath of statistically identical particles. The dynamics is described by Langevin equation with stochastic external force described by telegraphic…
We study the effect of freezing the positions of a fraction $c$ of particles from an equilibrium configuration of a supercooled liquid at a temperature $T$. We show that within the Random First-Order Transition theory pinning particles…
We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…
Recent experiments and computer simulations show that supercooled liquids around the glass transition temperature are "dynamically heterogeneous" [1]. Such heterogeneity is expected from the random first order transition theory of the glass…
A recently developed model of random walks on a $D$-dimensional hyperspherical lattice, where $D$ is {\sl not} restricted to integer values, is extended to include the possibility of creating and annihilating random walkers. Steady-state…
In this paper, we propose and analyze a novel one-dimensional inhomogeneous random walk model that combines spatial decay of transition probabilities with a temporal renewal structure for each excursion. In this model, the probability of…
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…