相关论文: Synchronization for discrete mean-field rotators

The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter…

Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns…

The aim of this paper is to provide a mathematical analysis of transformer architectures using a self-attention mechanism with layer normalization. In particular, observed patterns in such architectures resembling either clusters or uniform…

Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical…

We consider $n$-dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets…

In this work we extend the framework of monotone dynamical systems to a broad and important class of stochastic equations, namely cooperative McKean-Vlasov SDEs with multiplicative noise. Under a locally dissipative assumption, our main…

We report Brownian dynamics (BD) simulation and theoretical results for a system of spherical colloidal particles with permanent dipole moments in a rotating magnetic field. Performing simulations at a fixed packing fraction and dipole…

A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…

We propose and analyze numerical schemes for the gradient flow of $Q$-tensor with the quasi-entropy. The quasi-entropy is a strictly convex, rotationally invariant elementary function, giving a singular potential constraining the…

We study quantum dynamics of the rotationally driven Dicke model where the collective spin is rotated around the z axis with a finite velocity. In the absence of the rotating wave approximation we observe that for several physically…

In this letter a new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops with random precession frequencies. The model allows for an explicit study of orientational effects in…

Cellular automata lattice gases are useful systems for systematically exploring the connections between non-equilibrium statisitcal mechanics and dynamical systems theory. Here the chaotic properties of a Lorentz lattice gas are studied…

We explore systems of pulse-coupled oscillators beyond the mean-field limit [R.E. Mirollo and S.H. Strogatz, {SIAM J. Appl. Math.} {\bf 50}, 1645 (1990)] by means of a manageable description which leads to a great simplification of the…

We study, both analytically and numerically, the dynamics of mechanical oscillators kept in motion by a feedback force, which is generated electronically from a signal produced by the oscillators themselves. This kind of self-sustained…

A general approach for the description of correlated hopping in infinite dimensions, which is based on an expansion over electron hopping around the atomic limit, is developed. Such an approach keeps the dynamical mean-field theory local…

We consider the dynamics of a quantum directional reference frame undergoing repeated interactions. We first describe how a precise sequence of measurement outcomes affects the reference frame, looking at both the case that the measurement…

We present a review of our recent work in extending the successful dynamical mean-field theory from the equilibrium case to nonequilibrium cases. In particular, we focus on the problem of turning on a spatially uniform, but possibly time…

The physics of individual Q-balls and interactions between multiple Q-balls are well-studied in classical numerical simulations. Interesting properties and phenomena have been discovered, involving stability, forces, collisions and swapping…

Spontaneous synchronization is a remarkable collective effect observed in nature, whereby a population of oscillating units, which have diverse natural frequencies and are in weak interaction with one another, evolves to spontaneously…

A new approach is proposed which encompasses the dynamical mean field theory (DMFT) for strongly correlated electron systems and the self-consistent renormalization (SCR) theory of spin fluctuations. The latter is incorporated into DMFT as…