相关论文: Scaling dynamics of a cubic interval exchange tran…

The decimal expansion real numbers, familiar to us all, has a dramatic generalization to representation of dynamical system orbits by symbolic sequences. The natural way to associate a symbolic sequence with an orbit is to track its history…

We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing…

A study and numerical modeling of the cosmological evolution of a classical scalar field with the Higgs potential was carried out. Based on the formulated similarity properties of cosmological models, their main characteristics are studied…

We derive a stochastic nonlinear equation to describe the evolution and scaling properties of surfaces eroded by ion bombardment. The coefficients appearing in the equation can be calculated explicitly in terms of the physical parameters…

We consider a model of random permutations of the sites of the cubic lattice. Permutations are weighted so that sites are preferably sent onto neighbors. We present numerical evidence for the occurrence of a transition to a phase with…

We describe a 2 parameter family of polygon exchange transformations parameterized by points in a square. Whenever the two parameters are irrational, the polygon exchange has periodic orbits of arbitrarily large period. We show that for…

In this paper, we investigate the dynamics of the two-dimensional Ising model with stochastic resetting, utilizing a constant resetting rate procedure with zero-strength initial magnetization. Our results reveal the presence of a…

We study the time evolution of continuous-time quantum walks on randomly changing graphs. At certain moments edges of the graph appear or disappear with a given probability. We focus on the case when the time interval between subsequent…

When a system is driven across a quantum critical point at a constant rate its evolution must become non-adiabatic as the relaxation time $\tau$ diverges at the critical point. According to the Kibble-Zurek mechanism (KZM), the emerging…

Near a bifurcation point a system experiences critical slowing down. This leads to scaling behavior of fluctuations. We find that a periodically driven system may display three scaling regimes and scaling crossovers near a saddle-node…

A quantum many-body system can undergo transitions in the presence of continuous measurement. In this work, we find that a generic class of critical dynamical scaling behavior can emerge at these measurement-induced transitions. Remarkably,…

Scaling ideas and renormalization group approaches proved crucial for a deep understanding and classification of critical phenomena in thermal equilibrium. Over the past decades, these powerful conceptual and mathematical tools were…

We show how to turn the question of the absolute continuity of Bernoulli convolutions into one of counting the growth of the number of overlaps in the system. When the contraction parameter is a hyperbolic algebraic integer, we turn this…

Classical Bianchi-Lie, Backlund and Darboux transformations are considered. Their generalizations for the dynamical systems are discussed. For the transformation being the generalization of the normal shift the special class of dynamical…

We study the Anderson transition on a generic model of random graphs with a tunable branching parameter $1<K\le 2$, through large scale numerical simulations and finite-size scaling analysis. We find that a single transition separates a…

We describe numerical simulations of the stochastic diffusion equation with a conserved charge. We focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the…

We propose a discrete model to determine the metabolic scaling exponent based on Fibonacci growth patterns and discrete biological development phases. In contrast to continuous fractal models such as the West-Brown-Enquist (WBE) theory, the…

We present five-loop results for the renormalization of various models with a cubic interaction (in ${d = 6 - 2 \varepsilon}$ dimensions). For the scalar model and its ${O(n)}$-symmetric extension we provide renormalization constants,…

We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and…

We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and thus provides a rigorous numerical result (computer-assisted…