Related papers: Exploratory Behavior, Trap Models and Glass Transi…
In this paper we consider the one-dimensional, biased, randomly trapped random walk when the trapping times have infinite variance. We prove sufficient conditions for the suitably scaled walk to converge to a transformation of a stable…
We exploit a relation between the mean number $N_{m}$ of minima of random Gaussian surfaces and extreme eigenvalues of random matrices to understand the critical behaviour of $N_{m}$ in the simplest glass-like transition occuring in a toy…
Two models involving particles moving by ``hopping'' in disordered media are investigated: I) A model glass-forming liquid is investigated by molecular dynamics under (pseudo-) equilibrium conditions. ``Standard'' results such as mean…
The slowing down of molecular dynamics when approaching the glass transition generally proceeds much stronger than expected for thermally activated motions. This strange phenomenon can be formally ascribed to a temperature-dependent…
Dynamics near the surface of glasses is generally much faster than in the bulk. Neglecting static perturbations of structure at the surface, we use random first order transition theory to show the free energy barrier for activated motion…
We propose an interacting lattice gas model of structural glass characterized by particle distinguishability and site-particle-dependent random nearest-neighboring particle interactions. This incorporates disorder quenched in the…
The glass transition is considered as a phase transition in the system of topologically protected excitations in matter structure. The critical behavior of the system is considered both in statics and dynamics cases. It is shown in the…
We present a modified version of our "sliding model", where chain arcs, between two contacts at the surface, may move if all the barriers along the arc are weaker than a certain threshold.An important advance of the revised model is that…
A mesoscopic model is proposed to explain the anomalous dynamics in a supercooled liquid as its glass transition temperature is approached from above. The model is based on the assumption of $\beta$ organized $\alpha$ process, with the…
We study the dynamics of random walks hopping on homogeneous hyper-cubic lattices and multiplying at a fertile site. In one and two dimensions, the total number $\mathcal{N}(t)$ of walkers grows exponentially at a Malthusian rate depending…
We have considered the dynamical evolution of cellular patterns controlled by a stochastic Glauber process determined by the deviations of local cell topology from that of a crystalline structure. Above a critical temperature evolution is…
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 stark contrast with the conventional understanding of the glass transition, where the transition from glass to liquid appears as a dynamic process where atoms/molecules cooperatively relax into the equilibrium phase, we experimentally…
We study the glass transition by exploring a broad class of kinetic rules that can significantly modify the normal dynamics of super-cooled liquids, while maintaining thermal equilibrium. Beyond the usual dynamics of liquids, this class…
The mode-coupling theory for ideal glass transitions in simple systems is generalized to a theory for the glassy dynamics of molecular liquids using the density fluctuations of the sites of the molecule's constituent atoms as the basic…
Random walks describe diffusion processes, where movement at every time step is restricted to only the neighbouring locations. We construct a quantum random walk algorithm, based on discretisation of the Dirac evolution operator inspired by…
Dilute dipolar systems in three dimensions are expected to undergo a spin glass transition as the temperature decreases. Contrary to this, we find from Wang-Landau Monte Carlo simulations that at low concentrations $x$, dipoles randomly…
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…
We consider the Beta polymer, an exactly solvable model of directed polymer on the square lattice, introduced by Barraquand and Corwin. We study the statistical properties of its point to point partition sum. The problem is equivalent to a…
We consider a one-dimensional Brownian motion with diffusion coefficient $D$ in the presence of $n$ partially absorbing traps with intensity $\beta$, separated by a distance $L$ and evenly spaced around the initial position of the particle.…