Order statistics and the analytic determination of Lyapunov spectra of some classes of high-dimensional billiard systems

摘要

The dynamics of systems such as rarely interacting confined gases are dominated by wall collision events. Provided such events are a source of dynamical instability, we show that the ordering of the Lyapunov spectra of these systems is determined by the order statistics of the particles' speeds. For a two-dimensional gas of N hard disks, this amounts to characterizing the one half moment of the ordered lengths of a stick broken at random into N pieces. Interestingly, systematic errors cause numerical computation of Lyapunov spectra based on the Gram-Schmidt reorthonormalization algorithm to fail for such systems.