Synchronization of Chaotic Maps by Symmetric Common Noise

Synchronization of identical chaotic systems subjected to common noise has been the subject of recent research. Studies on several chaotic systems have shown that, the synchronization is actually induced by the non-zero mean of the noise, and symmetric noise with zero-mean cannot lead to synchronization. Here it is presented that synchronization can be achieved by {\sl zero-mean} noise in some chaotic maps with large convergence regions.Comment: 5 pages, 4 figure

Dynamics of a hole in the large--U Hubbard model: a Feynman diagram approach

We study the dynamics of a single hole in an otherwise half--filled two--dimensional Hubbard model by introducing a nonlocal Bogolyubov transformation in the antiferromagnetic state. This allows us to rewrite the Hamiltonian in a form that makes a separation between high--energy processes (involving double--occupancy) and low--energy physics possible. A diagrammatic scheme is developped that allows for a systematic study of the different processes delocalizing a carrier in the antiferromagnetic state. In particular, the so--called Trugman process, important if transverse spin fluctuations are neglected, is studied and is shown to be dominated by the leading vertex corrections. We analyze the dynamics of a single hole both in the Ising limit and with spin fluctuations. The results are compared with previous theories as well as with recent exact small--cluster calculations, and we find good agreement. The formalism establishes a link between weak and strong coupling methodologies.Comment: Latex 34pages, Orsay Preprint, submitted to Phys. Rev.

Non-linear Plasma Wake Growth of Electron Holes

An object's wake in a plasma with small Debye length that drifts \emph{across} the magnetic field is subject to electrostatic electron instabilities. Such situations include, for example, the moon in the solar wind wake and probes in magnetized laboratory plasmas. The instability drive mechanism can equivalently be considered drift down the potential-energy gradient or drift up the density-gradient. The gradients arise because the plasma wake has a region of depressed density and electrostatic potential into which ions are attracted along the field. The non-linear consequences of the instability are analysed in this paper. At physical ratios of electron to ion mass, neither linear nor quasilinear treatment can explain the observation of large-amplitude perturbations that disrupt the ion streams well before they become ion-ion unstable. We show here, however, that electron holes, once formed, continue to grow, driven by the drift mechanism, and if they remain in the wake may reach a maximum non-linearly stable size, beyond which their uncontrolled growth disrupts the ions. The hole growth calculations provide a quantitative prediction of hole profile and size evolution. Hole growth appears to explain the observations of recent particle-in-cell simulations