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

• Published in: Physica A Vol. 295; no. 3; pp. 391 - 408
• Main Authors: Vicentini, E, Kokshenev, V.B
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 15.06.2001
• Subjects: Anomalous diffusion; Coarse-graining; Open circle and square billiards; Relaxation channels; Survival probability; Transient dynamics; Relaxation channels; Coarse-graining; 42.65Sf; 0.5.45+b; Anomalous diffusion; Survival probability; 42.65An; Open circle and square billiards; Transient dynamics
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/S0378-4371(01)00138-8

We report on decay problem of classical systems. Mesoscopic level consideration is given on the basis of transient dynamics of non-interacting classical particles bounded in billiards. Three distinct decay channels are distinguished through the long-tailed memory effects revealed by temporal behavior of survival probability t − α : (i) the universal (independent of geometry, initial conditions and space dimension) channel with α=1 of Brownian relaxation of non-trapped regular parabolic trajectories and (ii) the non-Brownian channel α<1 associated with subdiffusion relaxation motion of irregular nearly trapped parabolic trajectories. These channels are common of non-fully chaotic systems, including the non-chaotic case. In the fully chaotic billiards the (iii) decay channel is given by α>1 due to “highly chaotic bouncing ball” trajectories. We develop a statistical approach to the problem, earlier proposed for chaotic classical systems (Physica A 275 (2000) 70). A systematic coarse-graining procedure is introduced for non-chaotic systems (exemplified by circle and square geometry), which are characterized by a certain finite characteristic collision time. We demonstrate how the transient dynamics is related to the intrinsic dynamics driven by the preserved Liouville measure. The detailed behavior of the late-time survival probability, including a role of the initial conditions and a system geometry, is studied in detail, both theoretically and numerically.