Related papers: Coarsening in inhomogeneous systems
A simplified Heisenberg spin model is studied in order to examine the idea of decoherence in closed quantum systems. For this purpose, we present a quantifiable definition to quantum coherence $\Xi$, and discuss in some detail a general…
We discuss the method of folding for discrete planar systems and use it to establish the existence or non-existence of cycles or chaos in planar systems of rational difference equations with variable coefficients. These include some systems…
In the corner-sharing lattice, magnetic frustration causes macroscopic degeneracy in the ground state, which prevents systems from ordering. However, if the ensemble of the degenerate configuration has some global structure, the system can…
We present the first analytical study of stability loss and evolution of domain structure in inhomogeneous ferroelectric samples for exactly solvable model. The model assumes a short-circuited capacitor with two regions with slightly…
We study the kinetics after a low temperature quench of the one-dimensional Ising model with long range interactions between spins at distance $r$ decaying as $r^{-\alpha}$. For $\alpha =0$, i.e. mean field, all spins evolve coherently…
In this review, we study some aspects of the non-equilibrium dynamics of quantum systems. In particular, we consider the effect of varying a parameter in the Hamiltonian of a quantum system which takes it across a quantum critical point or…
Ordered phases on curved substrates experience a complex interplay of ordering and intrinsic curvature, commonly producing frustration and singularities. This is an especially important issue in crystals as ever-smaller scale materials are…
Anomalous coarsening in far-from equilibrium one-dimensional systems is investigated by simulation and analytic techniques. The minimal hard core particle (exclusion) models contain mechanisms of aggregated particle diffusion, with rates…
Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…
The loss of coherence of a quantum system coupled to a heat bath as expressed by the reduced density matrix is shown to lead to the miss-characterization of some systems as being incoherent when they are not. The spin boson problem and the…
We provide a brief survey of quantum statistical characterisations of order, disorder and coherence in systems of many degrees of freedom. Here, order and coherence are described in terms of symmetry breakdown, while disorder is described…
We demonstrate the large scale effects of the interplay between shape and hard core interactions in a system with left- and right-pointing arrowheads ~$\textless ~~ \textgreater$~ on a line, with reorientation dynamics. This interplay leads…
This review is intended to give a pedagogical and unified view on the subject of the statistics and scaling of physical quantities in disordered electron systems at very low temperatures. Quantum coherence at low temperatures and randomness…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…
The Coulomb phase, with its dipolar correlations and pinch-point-scattering patterns, is central to discussions of geometrically frustrated systems, from water ice to binary and mixed-valence alloys, as well as numerous examples of…
In many growth processes particles are highly mobile in an active layer at the surface, but are relatively immobile once incorporated in the bulk. We study models in which atoms are allowed to interact, equilibrate, and order on the…
Coherence vortices are screw-type topological defects in the phase of Glauber's two-point degree of quantum coherence, associated with pairs of spatial points at which an ensemble-averaged stochastic quantum field is uncorrelated. Coherence…
We investigate the nonequilibrium dynamics and loss of coherence in a quantum impurity system using the spinless resonant level model subject to sudden quenches of the hybridization between the impurity and the metal. The survival…
Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…
This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…