Related papers: Topological chiral random walker
The scaling properties of a random walker subject to the global constraint that it needs to visit each site an even number of times are determined. Such walks are realized in the equilibrium state of one dimensional surfaces that are…
Phases of matter with non-trivial topological order are predicted to exhibit a variety of exotic phenomena, such as the existence robust localized bound states in 1D systems, and edge states in 2D systems, which are expected to display…
We consider Activated Random Walk (ARW), a particle system with mass conservation, on the cycle $\mathbb{Z}/n\mathbb{Z}$. One starts with a mass density $\mu>0$ of initially active particles, each of which performs a simple symmetric random…
Random walks provide a simple conventional model to describe various transport processes, for example propagation of heat or diffusion of matter through a medium. However, in many practical cases the medium is highly irregular due to…
We study the dynamical localization of discrete time evolution of topological split-step quantum random walk (QRW) on a single-site defect starting from a uniform distribution. Using analytical and numerical calculations, we determine the…
Synchronization of coupled oscillators is a ubiquitous phenomenon found throughout nature. Its robust realization is crucial to our understanding of various nonlinear systems, ranging from biological functions to electrical engineering. On…
Self-avoiding random walks on graphs can be seen as walkers interacting with their own past history. This letter considers a complementary class of dynamics: Mutual future avoiding random walks (MFARWs), where stochastically driven walkers…
The non-Bloch topology leads to the emergence of various counter-intuitive phenomena in non-Hermitian systems under the open boundary condition (OBC), which can not find a counterpart in Hermitian systems. However, in the non-Hermitian…
This paper proposes an attributed network growth model. Despite the knowledge that individuals use limited resources to form connections to similar others, we lack an understanding of how local and resource-constrained mechanisms explain…
The quantum-mechanical counterpart of a classical random walk offers a rich dynamics that has recently been shown to include topologically protected bound states (zero-modes) at boundaries or domain walls. Here we show that a topological…
A continuous-time quantum walk (CTQW) is sedentary if the return probability in the starting vertex is close to one at all times. Recent results imply that, when starting from a maximal degree vertex, the CTQW dynamics generated by the…
The aim of this paper is to deepen the analysis of the asymptotic behavior of the so-called minimal random walk (MRW) using a new martingale approach. The MRW is a discrete-time random walk with infinite memory that has three regimes…
Humans excel at robust bipedal walking in complex natural environments. In each step, they adequately tune the interaction of biomechanical muscle dynamics and neuronal signals to be robust against uncertainties in ground conditions.…
Traveling waves are ubiquitous in nature and control the speed of many important dynamical processes, including chemical reactions, epidemic outbreaks, and biological evolution. Despite their fundamental role in complex systems, traveling…
In this article, we present new random walk methods to solve flow and transport problems in unsaturated/saturated porous media, including coupled flow and transport processes in soils, heterogeneous systems modeled through random hydraulic…
Localized perturbations in a real-world network have the potential to trigger cascade failures at the whole system level, hindering its operations and functions. Standard approaches analytically tackling this problem are mostly based either…
I propose to study the complex physics of topological phases by an all optical implementation of a discrete-time quantum walk. The main novel ingredient is the use of parametric amplifiers in the random network which can in turn be used to…
We study the robustness of an evolving system that is driven by successive inclusions of new elements or constituents with $m$ random interactions to older ones. Each constitutive element in the model stays either active or is temporarily…
We show that dynamical clustering, where a system segregates into distinguishable subsets of synchronized elements, and chimera states, where differentiated subsets of synchronized and desynchronized elements coexist, can emerge in networks…
Discrete quantum walks are periodically driven systems with discrete time evolution. In contrast to ordinary Floquet systems, no microscopic Hamiltonian exists, and the one-period time evolution is given directly by a series of unitary…