Related papers: Scaling and width distributions of parity conservi…
We consider a one-dimensional two component extended Fermi-Hubbard model with nearest neighbor interactions and mass imbalance between the two species. We study the stability of trimers, various observables for detecting them, and expansion…
We compute the probability distribution of the interface width at the depinning threshold, using recent powerful algorithms. It confirms the universality classes found previously. In all cases, the distribution is surprisingly well…
Growth and roughness of the interface of deposited polymer chains driven by a field onto an impenetrable adsorbing surface are studied by computer simulations in (2+1) dimensions. The evolution of the interface width W shows a crossover…
We propose a unified scaling theory of entanglement entropy in the confinements of finite bond dimensions, dynamics and system sizes. Within the theory, the finite-entanglement scaling introduced recently is generalized to the dynamics…
We calculate universal finite-size scaling functions for systems with an n-component order parameter and algebraically decaying interactions. Just as previously has been found for short-range interactions, this leads to a singular…
To quantitatively characterize height distributions (HDs), one uses adimensional ratios of their first central moments ($m_n$) or cumulants ($\kappa_n$), especially the skewness $S$ and kurtosis $K$, whose accurate estimate demands an…
Height fluctuations of growing surfaces can be characterized by the probability distribution of height in a spatial point at a finite time. Recently there has been spectacular progress in the studies of this quantity for the…
We introduce a one-parameter deformation for one-dimensional (1D) quantum lattice models, the hyperbolic deformation, where the scale of the local energy is proportional to cosh lambda j at the j-th site. Corresponding to a 2D classical…
Power-law sensitivity to initial conditions at the edge of chaos provides a natural relation between the scaling properties of the dynamics attractor and its degree of nonextensivity as prescribed in the generalized statistics recently…
We introduce a class of (2+1)-dimensional stochastic growth processes, that can be seen as irreversible random dynamics of discrete interfaces. "Irreversible" means that the interface has an average non-zero drift. Interface configurations…
Synchronization problems in complex networks are very often studied by researchers due to its many applications to various fields such as neurobiology, e-commerce and completion of tasks. In particular, Scale Free networks with degree…
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
The effects of a randomly moving environment on a randomly growing interface are studied by the field theoretic renormalization group analysis. The kinetic growth of an interface (kinetic roughening) is described by the Kardar-Parisi-Zhang…
We propose and analyze a simple variational model for dislocations at semi-coherent interfaces. The energy functional describes the competition between two terms: a surface energy induced by dislocations that compensate the lattice misfit…
We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition. The scaling theory of localisation and the Anderson model of localisation are…
Relaxation of initially out-of-equilibrium rough interfaces in presence of thermal noise is investigated using Langevin formalism. During thermal equilibration towards the well-known roughening regime, three scaling regimes observed over…
Using different segmental dynamics and relaxation, characteristics of the interface growth is examined in an electrophoretic deposition of polymer chains on a three (2+1) dimensional discrete lattice with a Monte Carlo simulation.…
In this contribution we consider stochastic growth models in the Kardar-Parisi-Zhang universality class in 1+1 dimension. We discuss the large time distribution and processes and their dependence on the class on initial condition. This…