Related papers: Singular perturbation near mode-coupling transitio…
We present a quantitative theory for a relaxation function in a simple glass-forming model (binary mixture of particles with different interaction parameters). It is shown that the slowing down is caused by the competition between locally…
We construct and solve a classical percolation model with a phase transition that we argue acts as a proxy for the quantum many-body localisation transition. The classical model is defined on a graph in the Fock space of a disordered,…
We calculate for a binary mixture of Lennard-Jones particles the time dependence of the solution of the mode-coupling equations in which the full wave vector dependence is taken into account. In addition we also take into account the short…
We propose a method of classifying the operation of a system into finitely many modes. Each mode has its own objectives for the system's behaviour and its own mathematical models and algorithms designed to accomplish its objectives. A…
This work is motivated by a desire to understand transitions between stable equilibria observed in Stommel's 1961 thermohaline circulation model. We adapt the model, including a forcing parameter as a dynamic slow variable. The resulting…
The adaptive perturbation method decomposes a Hamiltonian by the diagonal elements and non-diagonal elements of the Fock state. The diagonal elements of the Fock state are solvable but can contain the information about coupling constants.…
We revisit the long time dynamics of the spherical fully connected $p = 2$-spin glass model when the number of spins $N$ is large but {\it finite}. At $T=0$ where the system is in a (trivial) spin-glass phase, and on long time scale $t…
Within the framework of the mode-coupling theory of super-cooled liquids, we investigate new phenomena in colloidal systems on approach to their glass transitions. When the inter-particle potential contains an attractive part, besides the…
For almost thirty years, mode-coupling theory has been the most widely discussed and used but also the most controversial theory of the glass transition. In this paper we briefly review the reasons for both its popularity and its…
We provide an analytical study of the coupling of short and long wavelength fluctuation modes during the initial phase of reheating in two field models like hybrid inflation. In these models, there is - at linear order in perturbation…
A new perturbation theory is proposed for studying finite-size effects near critical point of the $\phi^4$ model with a one-component order parameter. The new approach is based on the techniques of generating functional and functional…
We analyze a renormalized perturbation expansion around the mode-coupling theory of the glass transition. We focus on the long-time limit of the irreducible memory function. We discuss a renormalized diagrammatic expansion for this function…
Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary…
We develop a systematic extension of mode-coupling theory (MCT) that incorporates critical dynamical fluctuations. Starting from a microscopic diagrammatic theory, we identify dominant classes of divergent diagrams near the mode-coupling…
A mutilated model is constructed to approximate the collision term of spin Boltzmann equation that incorporates newly appearing collisional invariants i.e, the total angular momentum. With recourse to degenerate perturbation theory, the…
We apply topological methods to the study of the set of harmonic solutions of periodically perturbed autonomous ordinary differential equations on differentiable manifolds, allowing the perturbing term to contain a fixed delay. In the…
A prescription is developed for matching general relativistic perturbations across singularities of the type encountered in the ekpyrotic and cyclic scenarios i.e. a collision between orbifold planes. We show that there exists a gauge in…
Shear bands are narrow zones of intense shear observed during plastic deformations of metals at high strain rates. Because they often precede rupture, their study attracted attention as a mechanism of material failure. Here, we aim to…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
We calculate the power spectrum of curvature perturbations when the inflaton field is rolling over the top of a local maximum of a potential. We show that the evolution of the field can be decomposed into a late-time attractor, which is…