On survival dynamics of classical systems. Non-chaotic open billiards

We report on decay problem of classical systems. Mesoscopic level considera tion is given on the basis of transient dynamics of non-interacting classic al particles bounded in billiards. Three distinct decay channels are distin guished through the long-tailed memory effects revealed by temporal behavio r of survival probability t(-x): (i) the universal (independent of geometry , initial conditions and space dimension) channel with x=1 of Brownian rela xation of non-trapped regular parabolic trajectories and (ii) the non-Brown ian channel x <1 associated with subdiffusion relaxation motion of irregula r nearly trapped parabolic trajectories. These channels are common of non-f ully chaotic systems, including the non-chaotic case. In the fully chaotic billiards the (iii) decay channel is given by x >1 due to "highly chaotic b ouncing ball" trajectories. We develop a statistical approach to the proble m, earlier proposed for chaotic classical systems (Physica A 275 (2000) 70) . A systematic coarse-graining procedure is introduced for non-chaotic syst ems (exemplified by circle and square geometry), which are characterized by a certain finite characteristic collision time, We demonstrate how the tra nsient dynamics is related to the intrinsic dynamics driven by the preserve d Liouville measure, The detailed behavior of the late-time survival probab ility, including a role of the initial conditions and a system geometry, is studied in detail, both theoretically and numerically. (C) 2001 Elsevier S cience B.V, All rights reserved.