Probing rare physical trajectories with Lyapunov weighted dynamics

Details Probing rare physical trajectories with Lyapunov weighted dynamics Probing rare physical trajectories with Lyapunov weighted dynamics

2006-11-27

arxiv.org/abs/cond-mat/0611672v1

Nature Physics 3, 203 - 207 (2007)

Physics

Condensed Matter

Statistical Mechanics

Accepted for publication in Nature Physics. Due to size restrictions, the figures are not of high quality

Scientific paper

10.1038/nphys515

The transition from order to chaos has been a major subject of research since the work of Poincare, as it is relevant in areas ranging from the foundations of statistical physics to the stability of the solar system. Along this transition, atypical structures like the first chaotic regions to appear, or the last regular islands to survive, play a crucial role in many physical situations. For instance, resonances and separatrices determine the fate of planetary systems, and localised objects like solitons and breathers provide mechanisms of energy transport in nonlinear systems such as Bose-Einstein condensates and biological molecules. Unfortunately, despite the fundamental progress made in the last years, most of the numerical methods to locate these 'rare' trajectories are confined to low-dimensional or toy models, while the realms of statistical physics, chemical reactions, or astronomy are still hard to reach. Here we implement an efficient method that allows one to work in higher dimensions by selecting trajectories with unusual chaoticity. As an example, we study the Fermi-Pasta-Ulam nonlinear chain in equilibrium and show that the algorithm rapidly singles out the soliton solutions when searching for trajectories with low level of chaoticity, and chaotic-breathers in the opposite situation. We expect the scheme to have natural applications in celestial mechanics and turbulence, where it can readily be combined with existing numerical methods

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