Related papers: Synchronization for discrete mean-field rotators
We consider the natural Langevin dynamics which is reversible with respect to the mean-field plane rotator (or classical spin XY) measure. It is well known that this model exhibits a phase transition at a critical value of the interaction…
We study the dynamics of the many-body atomic kicked rotor with interactions at the mean-field level, governed by the Gross-Pitaevskii equation. We show that dynamical localization is destroyed by the interaction, and replaced by a…
A dynamic mean-field theory for spin ensembles (spinDMFT) at infinite temperatures on arbitrary lattices is established. The approach is introduced for an isotropic Heisenberg model with $S = \tfrac12$ and external field. For large…
The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N…
We introduce and study a nonlinear discrete dynamical system describing the evolution of a resource distribution among interacting agents. The model generalizes several classical mean-field and opinion-dynamics frameworks and is defined on…
We consider a nonlinear oscillator with state-dependent time-delay that displays a countably infinite number of nested limit cycle attractors, \emph{i.e.} megastability. In the low-memory regime, the equation reduces to a self-excited…
We consider non-linear evolution equations arising from mean-field limits of particle systems on discrete spaces. We investigate a notion of curvature bounds for these dynamics based on convexity of the free energy along interpolations in a…
We consider a large number $N$ of quantum particles coupled via a mean field interaction to another quantum system (reservoir). Our main result is an expansion for the averages of observables, both of the particles and of the reservoir, in…
We investigate the quench dynamics of the transverse field Ising model on a finite fully connected lattice as a prime example of non-equilibrium mean field dynamics. Using a rate function approach we compute the leading order corrections to…
We explore the synchronization phenomenon in the quantum few-body system of spins with the non-local dissipation. Without the external driving, we find that the system can exhibit stable oscillatory behaviors in the long-time dynamics…
We present a generalized dynamical mean-field approach for the nonequilibrium physics of a strongly correlated system in the presence of a time-dependent external field. The Keldysh Green's function formalism is used to study the…
Relationships between general long-range interacting classical systems on a lattice and the corresponding mean-field models (infinitely long-range interacting models) are investigated. We study systems in arbitrary dimension d for periodic…
We introduce the Random Quadratic Form (RQF): a stochastic differential equation which formally corresponds to the gradient flow of a random quadratic functional on a sphere. While the one-point dynamics of the system is a Brownian motion…
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…
This work explores a synchronization-like phenomenon induced by common noise for continuous-time Markov jump processes given by chemical reaction networks. A corresponding random dynamical system is formulated in a two-step procedure, at…
We derive and study stochastic dissipative dynamics on coadjoint orbits by incorporating noise and dissipation into mechanical systems arising from the theory of reduction by symmetry, including a semidirect-product extension. Random…
Many systems in biology, physics and chemistry can be modeled through ordinary differential equations, which are piecewise smooth, but switch between different states according to a Markov jump process. In the fast switching limit, the…
During the past decades, the question of existence and properties of a random attractor of a random dynamical system generated by an S(P)DE has received considerable attention, for example by the work of Gess and R\"ockner. Recently some…
We analyze a non-Markovian mean field interacting spin system, related to the Curie--Weiss model. We relax the Markovianity assumption by replacing the memoryless distribution of the waiting times of a classical spin-flip dynamics with a…
We analyze the collective behavior of a lattice model of pulse-coupled oscillators. By means of computer simulations we find the relation between the intrinsic dynamics of each member of the population and their mutual interaction that…