Space-time properties of Gram-Schmidt vectors in classical Hamiltonian evolution.
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.
Green
Jason R
JR
Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge, United Kingdom. jg525@cam.ac.uk
Jellinek
Julius
J
Berry
R Stephen
RS
D000465:Algorithms; D001703:Biophysics / Q000379:methods*; D016000:Cluster Analysis; D003198:Computer Simulation; D019277:Entropy; D007700:Kinetics; D015233:Models, Statistical; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D010825:Physics / Q000379:methods*