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The Hegselmann-Krause (HK) model is a typical self-organizing system with local rule dynamics. In spite of its widespread use and numerous extensions, the underlying theory of its synchronization induced by noise still needs to be…
Recently the theory of noise-induced synchronization of Hegselmann-Krause (HK) dynamics has been well developed. As a typical opinion dynamics of bounded confidence, the HK model obeys a synchronous updating rule, i.e., \emph{all} agents…
The mixed Hegselmann-Krause (HK) model covers the synchronous Hegselmann-Krause model, the asynchronous Hegselmann-Krause model and the Deffuant model. Previous study~\cite{mHK, mHK2} deals with the mixed HK model on finite graphs. In the…
We study convergence of the following discrete-time non-linear dynamical system: n agents are located in R^d and at every time step, each moves synchronously to the average location of all agents within a unit distance of it. This popularly…
The classic Hegselmann-Krause (HK) model for opinion dynam- ics consists of a set of agents on the real line, each one instructed to move, at every time step, to the mass center of all the agents within a fixed distance R. In this work, we…
A new type of noise-induced synchronous behavior is described. This phenomenon, called incomplete noise-induced synchronization, arises for one-dimensional Ginzburg-Landau equations driven by common noise. The mechanisms resulting in the…
Environmental noise can hinder the metrological capabilities of entangled states. While the use of entanglement allows for Heisenberg-limited resolution, the largest permitted by quantum mechanics, deviations from strictly unitary dynamics…
Strongly interacting quantum many-body systems are expected to thermalize, however, some evade thermalization due to symmetries. Quantum synchronization provides one such example of ergodicity breaking, but previous studies have focused on…
We propose a quantum analogue of the Huygens clock, in which the phases of two spins achieve synchronization through their interaction with a shared environment. The environment functions analogously to the escapement mechanism in a…
In this thesis we study synchronization phenomena in natural and artificial coupled multi-component systems, applicable to the scalability of parallel discrete-event simulation for systems with asynchronous dynamics. We analyze the…
We consider the Hegselmann-Krause dynamics on a one-dimensional torus and provide the first proof of convergence of this system. The proof requires only fairly minor modifications of existing methods for proving convergence in Euclidean…
Non-classical resources enable measurements to achieve a precision that exceeds the limits predicted by the central limit theorem. However, environmental noise arising from system-environment interactions severely limits the performance of…
The process of pattern formation in the two dimensional Swift-Hohenberg equation is examined through numerical and analytic methods. Dynamic scaling relationships are developed for the collective ordering of convective rolls in the limit of…
Quantum noise correlations have been employed in several areas in physics including condensed matter, quantum optics and ultracold atom to reveal non-classical states of the systems. So far, such analysis mostly focused on systems in…
We study the role played by noise on the QW introduced in [1], a 1D model that is inspired by a two particle interacting QW. The noise is introduced by a random change in the value of the phase during the evolution, from a constant…
The theory of quasifree quantum stochastic calculus for infinite-dimensional noise is developed within the framework of Hudson-Parthasarathy quantum stochastic calculus. The question of uniqueness for the covariance amplitude with respect…
In this paper, we study geometric features of orientation-preserving random dynamical systems on the circle driven by memoryless noise that exhibit stable synchronisation: we consider crack points, invariant measures, and the link between…
In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work…
The Vicsek model has long stood as a pivotal framework in exploring collective behavior and self-organization, captivating the scientific community with its compelling dynamics. However, understanding how noise influences synchronization…
Physics deals with Newtonian particles described by position q and momentum p. The precision of the simultaneous measurement of q and p is limited by the uncertainty relation ruled by Planck's constant. From the uncertainty relation all…