Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · nlin/0305056

Stochastic stabilization of cosmological photons

C. P. Dettmann·J. P. Keating·S. D. Prado
View original source ↗Read source document ↗Export metadata ↓

Abstract

The stability of photon trajectories in models of the Universe that have constant spatial curvature is determined by the sign of the curvature: they are exponentially unstable if the curvature is negative and stable if it is positive or zero. We demonstrate that random fluctuations in the curvature provide an additional stabilizing mechanism. This mechanism is analogous to the one responsible for stabilizing the stochastic Kapitsa pendulum. When the mean curvature is negative it is capable of stabilizing the photon trajectories; when the mean curvature is zero or positive it determines the characteristic frequency with which neighbouring trajectories oscillate about each other. In constant negative curvature models of the Universe that have compact topology, exponential instability implies chaos (e.g. mixing) in the photon dynamics. We discuss some consequences of stochastic stabilization in this context.

Explore related subjects

nlin.CDastro-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

C. P. Dettmann, J. P. Keating, S. D. Prado. 2004-06-24. Stochastic stabilization of cosmological photons. https://doi.org/10.1088/0305-4470%2F37%2F30%2Fl03

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Relativistic Quantum Chaos in Neutrino Billiards

Neutrino billiards serve as a model system for the study of aspects of relativistic quantum chaos. These are relativistic quantum billiards consisting of a spin-1/2 particle which is confined to a planar domain by imposing boundary conditions on the spinor components which were proposed in [Berry and Mondragon, {\it Proc. R. Soc.} A {\bf 412}, 53 (1987)]. We review their general features and the properties of neutrino billiards with shapes of billiards with integrable dynamics. Furthermore, we review the features of two neutrino billiards with the shapes of billiards generating a chaotic dynamics, whose nonrelativistic counterpart exhibits particular properties. Finally we briefly discuss possible experimental realizations of relativistic quantum billiards based on graphene billiards, that is, finite-size sheets of graphene.

nlin.CD↗
arXiv2026

Butterfly Effects in Turbulence: A Unified View through the Finite Size Lyapunov Exponent

The ``butterfly effect'', introduced over half a century ago by Edward Lorenz, has shifted from a cornerstone of dynamical systems to a popular metaphor, yet its true physical manifestation in fully developed turbulence spans a spectrum of phenomena from standard sensitivity on initial conditions to the recently established concept of Eulerian spontaneous stochasticity. Here, we propose an attempt at a systematic synthesis that brings these different but interconnected ideas together within the unifying framework of the Finite Size Lyapunov Exponent (FSLE). The FSLE describes the growth rate of perturbations as a function of their scale, enabling a comprehensive characterization of the multiscale physics of turbulent flows. Using the FSLE and the Sabra shell model, extended to include thermal noise, we bridge the classical, small-scale Lyapunov regime with predictability at large scales and its interpretation in terms of Eulerian spontaneous stochasticity. Moreover, using the FSLE and the Kraichnan model, we also illustrate the closely related phenomenon of Lagrangian spontaneous stochasticity. To complete the spectrum of butterfly effects, we also examine the ``literal butterfly'' scenario of localized, sub-dissipative perturbations.

nlin.CD↗
arXiv2026

A comparison of three models of a whirling string as it becomes chaotic

A stretched wire driven near its fundamental frequency can leave the plane of the driving force and whirl. At larger amplitudes the whirl becomes modulated, reverses its direction, and becomes chaotic. Three models of this motion are in common use: the geometrically exact string equations; a two-mode model -- the Kirchhoff-Carrier equation with one transverse mode in each plane; and the averaged equations for the slow amplitudes of those two modes. We integrate all three under similar conditions and compare them along the route to chaos, which starts with a Hopf bifurcation of the steady whirl and passes through period doublings to chaotic attractors organized by a Shil'nikov homoclinic orbit. The small parameter of the averaging, the ratio $\varepsilon = c/ω_1$ of the modulation rate to the fundamental frequency, runs from 0.005 to 0.02. Qualitatively the three models agree in the sequence of bifurcations, the coexisting attractors, the return maps and the Lyapunov exponents. Quantitatively, averaging places each local bifurcation $0.7\varepsilon$ to $1.2\varepsilon$ higher in the scaled detuning. The geometrically exact and two-mode models agree with each other to within 0.002 at the local bifurcations for $\varepsilon \le 0.01$. The Shil'nikov ratio, which decides whether chaos accompanies the homoclinic orbit, agrees among the three models to within 1.5% for $\varepsilon \le 0.01$, yet the homoclinic bifurcation itself moves by about $\varepsilon$ at the lower damping and by 6 to 9 times $\varepsilon$ at the higher; the difference is set by how quickly the return of the homoclinic loop changes with detuning.

nlin.CD↗