Cosmic time and chaos

It is shown that the Friedman cosmological models (1) with bulk viscosity dissipation, (2) with Weyssenhoff fluid (perfect fluid with macroscopic spin), (3) with a phase transition in a very early stage of the evolution, all possessing negative space-curvature, after being compactified. exhibit chaotic behaviour in asymptotic states. Geodesic flows in such models are characterized by an exponential instability; they are mixing ergodic, and have non-zero metric entropy. In fact these world models are special cases of a "chaotic evolution" described by Lockhart, Misra and Prigogine. In particular, Prigogine’s "internal time" may be defined in them. Some remarks, concerning a predictability in cosmological models with the geodesic instability, are made

Acoustics of early universe. I. Flat versus open universe models

A simple perturbation description unique for all signs of curvature, and based on the gauge-invariant formalisms is proposed to demonstrate that: (1) The density perturbations propagate in the flat radiation-dominated universe in exactly the same way as electromagnetic or gravitational waves propagate in the epoch of the matter domination. (2) In the open universe, sounds are dispersed by curvature. The space curvature defines the minimal frequency $\omega_{\rm c}$ below which the propagation of perturbations is forbidden. Gaussian acoustic fields are considered and the curvature imprint in the perturbations spectrum is discussed.Comment: The new version extended by 2 sections. Changes in notation. Some important comments adde

Evolution of density perturbations in a realistic universe

Prompted by the recent more precise determination of the basic cosmological parameters and growing evidence that the matter-energy content of the universe is now dominated by dark energy and dark matter we present the general solution of the equation that describes the evolution of density perturbations in the linear approximation. It turns out that as in the standard CDM model the density perturbations grow very slowly during the radiation dominated epoch and their amplitude increases by a factor of about 4000 in the matter and later dark energy dominated epoch of expansion of the universe.Comment: 19 pages, 4 figure

Dynamical Systems Approach to Magnetised Cosmological Perturbations

Assuming a large-scale homogeneous magnetic field, we follow the covariant and gauge-invariant approach used by Tsagas and Barrow to describe the evolution of density and magnetic field inhomogeneities and curvature perturbations in a matter-radiation universe. We use a two parameter approximation scheme to linearize their exact non-linear general-relativistic equations for magneto-hydrodynamic evolution. Using a two-fluid approach we set up the governing equations as a fourth order autonomous dynamical system. Analysis of the equilibrium points for the radiation dominated era lead to solutions similar to the super-horizon modes found analytically by Tsagas and Maartens. We find that a study of the dynamical system in the dust-dominated era leads naturally to a magnetic critical length scale closely related to the Jeans Length. Depending on the size of wavelengths relative to this scale, these solutions show three distinct behaviours: large-scale stable growing modes, intermediate decaying modes, and small-scale damped oscillatory solutions.Comment: 15 pages RevTeX, 5 figures. Accepted for publication in Physical Review

Unraveling quantum Hall breakdown in bilayer graphene with scanning gate microscopy

We use low-temperature scanning gate microscopy (SGM) to investigate the breakdown of the quantum Hall regime in an exfoliated bilayer graphene flake. SGM images captured during breakdown exhibit intricate patterns of "hotspots" where the conductance is strongly affected by the presence of the tip. Our results are well described by a model based on quantum percolation which relates the points of high responsivity to tip-induced scattering between localized Landau levels.Comment: 6 pages, 4 figure

LARGE SCALE PERTURBATIONS IN THE OPEN UNIVERSE

When considering perturbations in an open (Omega<1) universe, cosmologists retain only sub-curvature modes (defined as eigenfunctions of the Laplacian whose eigenvalue is less than -1 in units of the curvature scale, in contrast with the super-curvature modes whose eigenvalue is between -1 and 0). Mathematicians have known for almost half a century that all modes must be included to generate the most general HOMOGENEOUS GAUSSIAN RANDOM FIELD, despite the fact that any square integrable FUNCTION can be generated using only the sub-curvature modes. The former mathematical object, not the latter, is the relevant one for physical applications. The mathematics is here explained in a language accessible to physicists. Then it is pointed out that if the perturbations originate as a vacuum fluctuation of a scalar field there will be no super-curvature modes in nature. Finally the effect on the cmb of any super-curvature contribution is considered, which generalizes to Omega<1 the analysis given by Grishchuk and Zeldovich in 1978. A formula is given, which is used to estimate the effect. In contrast with the case Omega=1, the effect contributes to all multipoles, not just to the quadrupole. It is important to find out whether it has the same l dependence as the data, by evaluating the formula numerically.Comment: 31 page

Detection And Transcription Of New Words

This paper describes a model which enables a speech recognition system to automatically detect new words and to provide a rough phonetic transcription. In our approach to the new word problem the decision whether new words occurred in the speech input is not based exclusively on acoustic evidence but also on a language model designed to support the detection of new words. We describe preliminary experiments to create new word grammars on the Wall Street Journal task. Furthermore we present recognition results of our new word model using the recognition engine of the JANUS speech to speech translation system [1, 2], designed around the task of conference registration. 1. INTRODUCTION The design of a speech recognition system for real applications requires addressing the new word problem since it is impossible to create vocabularies with 100% coverage of spontaneous input. The ability to detect and transcribe new words would enable a speech recognition system to handle their occurrence..