Related papers: Order parameter analysis of synchronization transi…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
The functional defined as the squared modulus of the spatial average of the wave function squared, plays the role of an ``order parameter'' for the transition between Hamiltonian ensembles with orthogonal and unitary symmetry. Upon breaking…
We present an extension of Landau's theory of phase transitions by incorporating the topology of the order parameter. When the order parameter comprises several components arising from multiplicity in the same irreducible representation of…
The long-term mean-field dynamics of coupled underdamped Duffing oscillators driven by an external periodic signal with Gaussian noise is investigated. A Boltzmann-type H-theorem is proved for the associated nonlinear Fokker-Planck equation…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…
Topological order is defined by topological invariants, rather than symmetries and local order parameters. Nonetheless some topological phases can be characterized by string order parameters and entanglement. In this article we study how…
The phase ordering properties of lattices of band-chaotic maps coupled diffusively with some coupling strength $g$ are studied in order to determine the limit value $g_e$ beyond which multistability disappears and non-trivial collective…
We explore quantum phase transitions using two probes of quantum chaos: out-of-time-order correlators (OTOCs) and the $r$-parameter obtained from the level spacing statistics. In particular, we address $p$-spin models associated with…
A system of five ordinary differential equations is studied which combines the Lorenz-84 model for the atmosphere and a box model for the ocean. The behaviour of this system is studied as a function of the coupling parameters. For most…
We study a system of dynamical units, each of which shows excitable or oscillatory behavior, depending on the choice of parameters. When we couple these units with repressive bonds, we can control the duration of collective oscillations for…
We consider ensembles of sine-coupled phase oscillators consisting of subpopulations of identical units, with a general heterogeneous coupling between subpopulations. Using the Watanabe-Strogatz ansatz we reduce the dynamics of the ensemble…
Using ultrashort laser pulses, it has become possible to probe the dynamics of long-range order in solids on microscopic timescales. In the conventional description of symmetry-broken phases within time-dependent Ginzburg-Landau theory, the…
We introduce an adaptation algorithm by which an ensemble of coupled oscillators with attractive and repulsive interactions is induced to adopt a prescribed synchronized state. While the performance of adaptation is controlled by measuring…
Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order…
Complex interactions leading to phase transitions continue to hold a due interest in the scientific community. We charactersize a phase transition in a coupled oscillators model where interactions are not local in nature. At a first order…
We introduce a general scheme for constructing order parameters (OPs) by extracting generic patterns from the dominant Fock states of many-body ground states. While topological phases are traditionally characterized by non-local invariants,…
Many natural and human-made complex systems feature group interactions that adapt over time in response to their dynamic states. However, most of the existing adaptive network models fall short of capturing these group dynamics, as they…
Theoretical and experimental study of high-acceleration patterns in vibrated granular layers is presented. The order parameter model based on parametric Ginzburg-Landau equation is used to describe strongly nonlinear excitations including…
We elucidate the relation between out-of-time-order correlators (OTOCs) and quantum phase transitions via analytically studying the OTOC dynamics in a degenerate spectrum. Our method points to key ingredients to dynamically detect quantum…
Out-of-time-ordered correlation functions (OTOCs) play a crucial role in the study of thermalization, entanglement, and quantum chaos, as they quantify the scrambling of quantum information due to complex interactions. As a consequence of…