Related papers: Dynamics of Influence on Hierarchical Structures

We discuss analytical approximation schemes for the dynamics of diluted spin models. The original dynamics of the complete set of degrees of freedom is replaced by a hierarchy of equations including an increasing number of global…

The stability of a leadership against a growing internal opposition is studied in bottom-up hierarchical organizations. Using a very simple model with bottom-up majority rule voting, the dynamics of power distribution at the various…

We introduce a simple model of static networks, where nodes are located on a ring structure, and two accompanying dynamic rules of repeated averaging on periodic node states. We assume nodes can interact with neighbors, and will add…

We investigate the connection between pseudo-Hermitian and Hermitian descriptions for a lattice, which consists of a set of isomorphic pseudo-Hermitian clusters. We show that such non-Hermitian systems can act as Hermitian systems. This is…

We study the Lebwohl-Lasher model for systems in which spin are arranged on random graph lattices. At equilibrium our analysis follows the theory of spin-systems on random graphs which allows us to derive exact bifurcation conditions for…

The ability of groups to make accurate collective decisions depends on a complex interplay of various factors, such as prior information, biases, social influence, and the structure of the interaction network. Here, we investigate a spin…

In mixed systems, besides regular and chaotic states, there are states supported by the chaotic region mainly living in the vicinity of the hierarchy of regular islands. We show that the fraction of these hierarchical states scales as…

The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimension. Here we study one of the simplest classical interacting lattice models, the nearest-neighbour…

We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a…

Topological phases are greatly enriched by including non-Hermiticity. While most works focus on the topology of the eigenvalues and eigenstates, how topologically nontrivial non-Hermitian systems behave in dynamics has only drawn limited…

Discrete-time regulatory networks are dynamical systems on directed graphs, with a structure inspired on natural systems of interacting units. There is a natural notion of determination amongst vertices, which we use to classify the nodes…

Hierarchy is one of the most conspicuous features of numerous natural, technological and social systems. The underlying structures are typically complex and their most relevant organizational principle is the ordering of the ties among the…

Surface states of a tight-binding model with nearest-neighbor hopping on a diamond lattice of finite thickness are investigated. We consider systems with (001), (110), and (111) surfaces. Even if the surface direction is fixed, there is…

The appearance of quasiparticle excitations with fractional statistics is a remarkable defining trait of topologically ordered systems. In this work, we investigate the experimentally relevant finite temperature regime in which one species…

A unified model of molecular and atomistic spin dynamics is presented enabling simulations both in microcanonical and canonical ensembles without the necessity of additional phenomenological spin damping. Transfer of energy and angular…

We present a numerical study of the dynamics of a non-ideal fluid subject to a density-dependent pseudo-potential characterized by a hierarchy of nested attractive and repulsive interactions. It is shown that above a critical threshold of…

We investigate the quantum dynamics of the electron spin resonance of topological defects (edge state) in dimerized chains. These objects are discontinuities of the spin chain protected by the properties of the global system leading to a…

A central question in dynamics is whether the topology of a system determines its geometry. This is known as rigidity. Under mild topological conditions rigidity holds for many classical cases, including: Kleinian groups, circle…

A fermionic model, built up of q species of localized Fermi particles, interacting by charge correlations, is isomorphic to a spin-q/2 Ising model. However, the equivalence is only formal and the two systems exhibit a different physical…

We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…