Space-time properties of Gram-Schmidt vectors in classical Hamiltonian evolution

作者：Green Jason R^*; Jellinek Julius; Berry R Stephen

来源：Physical Review E, 2009, 80(6): 066205.

DOI：10.1103/PhysRevE.80.066205

• atomic clusters
• chaos
• many-body problems
• nonlinear dynamical systems
• potential energy surfaces
• statistical mechanics
• vectors

Not all tangent space directions play equivalent roles in the local chaotic motions of classical Hamiltonian many-body systems. These directions are numerically represented by basis sets of mutually orthogonal Gram-Schmidt vectors, whose statistical properties may depend on the chosen phase space-time domain of a trajectory. We examine the degree of stability and localization of Gram-Schmidt vector sets simulated with trajectories of a model three-atom Lennard-Jones cluster. Distributions of finite-time Lyapunov exponent and inverse participation ratio spectra formed from short-time histories reveal that ergodicity begins to emerge on different time scales for trajectories spanning different phase-space regions, in a narrow range of total energy and history length. Over a range of history lengths, the most localized directions were typically the most unstable and corresponded to atomic configurations near potential landscape saddles.

• 出版日期2009-12