Related papers: Geometric Phase of Stochastic Oscillators
Stochastic resonance is a general phenomenon usually observed in one-dimensional, amplitude modulated, bistable systems.We show experimentally the emergence of phase stochastic resonance in the bidimensional response of a forced…
We study the stability of a stochastic oscillator whose frequency is a random process with finite time memory represented by an Ornstein-Uhlenbeck noise. This system undergoes a noise-induced bifurcation when the amplitude of the noise…
In an open system, the geometric phase should be described by a distribution. We show that a geometric phase distribution for open system dynamics is in general ambiguous, but the imposition of reasonable physical constraints on the…
We investigate phase synchronization between two identical or detuned response oscillators coupled to a slightly different drive oscillator. Our result is that phase synchronization can occur between response oscillators when they are…
Quantum phase transition is one of the main interests in the field of condensed matter physics, while geometric phase is a fundamental concept and has attracted considerable interest in the field of quantum mechanics. However, no relevant…
The synchronization of rhythms is ubiquitous in both natural and engineered systems, and the demand for data-driven analysis is growing. When rhythms arise from limit cycles, phase reduction theory shows that their dynamics are universally…
We propose a general framework of the geometric-phase interpretation for counting statistics. Counting statistics is a scheme to count the number of specific transitions in a stochastic process. The cumulant generating function for the…
We examine the dynamic and geometric phases of the electron in quantum mechanics using Hestenes' spacetime algebra formalism. First the standard dynamic phase formula is translated into the spacetime algebra. We then define new formulas for…
As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests…
Geometric phases describe how in a continuous-time dynamical system the displacement of a variable (called phase variable) can be related to other variables (shape variables) undergoing a cyclic motion, according to an area rule. The aim of…
This article studies stochastic relative phase stability, i.e., stochastic phase-cohesiveness, of discrete-time phase-coupled oscillators. Stochastic phase-cohesiveness in two types of networks is studied. First, we consider oscillators…
By characterizing the phase dynamics in coupled oscillators, we gain insights into the fundamental phenomena of complex systems. The collective dynamics in oscillatory systems are often described by order parameters, which are insufficient…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
Geometric phases arise naturally in a variety of quantum systems with observable consequences. They also arise in quantum computations when dressed states are used in gating operations. Here we show how they arise in these gating operations…
The relation between the geometric phase and quantum phase transition has been discussed in the Lipkin-Meshkov-Glick model. Our calculation shows the ability of geometric phase of the ground state to mark quantum phase transition in this…
The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases…
The phase-space of a simple synchronization model is thoroughly investigated. The model considers two-mode stochastic oscillators, coupled through a pulse-like interaction controlled by simple optimization rules. A complex phase space is…
The geometric phase is of fundamental interest and plays an important role in quantum information processing. However, the definition and calculation of this phase for open systems remains a problem due to the lack of agreement on…
We study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: i) phase noise acting…
Biological systems can rely on collective formation of a metachronal wave in an ensemble of oscillators for locomotion and for fluid transport. We consider one-dimensional chains of phase oscillators with nearest neighbor interactions,…