Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · nlin/0312051

Goldstone modes in Lyapunov spectra of hard sphere systems

Astrid S. de Wijn·Henk van Beijeren
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this paper, we demonstrate how the Lyapunov exponents close to zero of a system of many hard spheres can be described as Goldstone modes, by using a Boltzmann type of approach. At low densities, the correct form is found for the wave number dependence of the exponents as well as for the corresponding eigenvectors in tangent-space. The predicted values for the Lyapunov exponents belonging to the transverse mode are within a few percent of the values found in recent simulations, the propagation velocity for the longitudinal mode is within 1%, but the value for the Lyapunov exponent belonging to the longitudinal mode deviates from the simulations by 30%. For higher densities, the predicted values deviate more from the values calculated in the simulations. These deviations may be due to contributions from ring collisions and similar terms, which, even at low densities, can contribute to the leading order.

Explore related subjects

nlin.CD

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Astrid S. de Wijn, Henk van Beijeren. 2004-04-29. Goldstone modes in Lyapunov spectra of hard sphere systems. https://doi.org/10.1103/physreve.70.016207

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

KEEP EXPLORING

Related papers

arXiv2026

Reservoir Computing with a single Josephson junction

Physical reservoir computing exploits the nonlinear dynamics of a physical system to perform information processing tasks. Josephson junctions (JJs), as nonlinear superconducting devices with rich dynamical behavior, represent promising yet relatively unexplored candidates for reservoir computing. In this work, we demonstrate for the first time that a single Josephson junction can be employed as a reservoir computing substrate without the use of an explicit delay loop. Using numerical simulations, we analyze the reservoir performance in different dynamical regimes and show that optimal performance is achieved when the JJ operates in a stable yet responsive regime. Despite the absence of delayed feedback, the JJ exhibits sufficient memory through its intrinsic dynamics to achieve good performance on a chaotic time series prediction task. The underlying mechanism is analogous, at the dynamical level, to that of a driven nonlinear pendulum, highlighting the generality of the approach to other nonlinear oscillators. In addition, we explore an alternative input masking approach based on continuous modulation, highlighting its compatibility with practical implementations. These results establish Josephson junctions as a viable and efficient platform for reservoir computing and open the way to ultrafast, low-dissipation hardware realizations.

nlin.CD↗
arXiv2026

Risk-Sensitive Learning in Population Games under Extreme Events: Bifurcations and Chaotic Dynamics

Inspired by nonequilibrium phenomena in game dynamics and behavioral evidence on the impact of extreme events on decision making, we investigate the nonlinear dynamics of a discrete-time multiagent learning rule in population congestion games under extreme events affecting one of the actions. The population state, following a risk-sensitive variant of the Multiplicative Weights Update (MWU), is coupled with a belief variable capturing the agents perceived risk and updated through an adaptive expectation rule. We perform a two-parameter bifurcation analysis with respect to the agents controlled parameters, identifying regions of qualitatively distinct behavior. Equilibria are studied first from both game-theoretic and dynamical perspectives. The resulting two-dimensional system exhibits complex behavior, including multi-stability among fixed points, invariant curves, periodic and chaotic attractors. Despite this complexity, the attractors can be grouped into distinct families, while the Cesàro averages of the trajectories are shown to converge to the stationary equilibrium. The incorporation of risk associated with the extreme event leads to new dynamical phenomena: attracting invariant curves arise and give rise to phase-locking Arnold tongues, within which the dynamics is qualitatively similar. In this setting, codimension-two resonances are identified as organizing centers, both within individual tongues and along the bifurcation curves associated with the fixed-point family. Chaotic attractors emerge and are destroyed through Feigenbaum cascades and forward or reverse boundary crises, with interior and merging crises also observed, along with transient chaos and narrow periodic windows. For each qualitatively distinct region, representative phase portraits and the associated basins of attraction are examined.

nlin.CD↗
arXiv2026

Intermittency-induced transitions in fast-slow dynamical systems

Intermittent dynamics are ubiquitous in the Earth system and often arise from the interaction of processes evolving on different time scales. In this work, we investigate how intermittent bursts in a fast forcing system propagate to and reshape the dynamics of a slower response system that would otherwise settle onto a quasi-stationary or weakly oscillatory regime. We address this question in two coupled models of increasing complexity: a low-dimensional Lorenz-63 system and the spatially extended Kuramoto-Sivashinsky equation. Across both systems, intermittency in the forcing progressively reshapes the attractor of the slow response system and drives it into different regimes. Using the Wasserstein distance, we show that increasing the frequency of intermittent events progressively displaces the response attractor from its unperturbed counterpart, up to a limit beyond which this deviation saturates. We then show that varying the forcing intensity and the time-scale separation between the forcing and response systems drives distinct regime transitions, which we characterize through the variance of ensemble maxima, the power spectra of both systems, and extreme value statistics. Finally, we examine how the type of intermittency in the forcing system affects synchronization between the two systems through local phase locking, showing that specific transitions in the phase-locking behavior are tied to the underlying intermittency regime, and that the response delay scales exponentially with the time-scale separation.

nlin.CD↗