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

E Vicentini and V.b Kokshenev

Physica A: Statistical Mechanics and its Applications, 2001, vol. 295, issue 3, 391-408

Abstract: 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.

Keywords: Transient dynamics; Survival probability; Open circle and square billiards; Relaxation channels; Coarse-graining; Anomalous diffusion (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:295:y:2001:i:3:p:391-408

DOI: 10.1016/S0378-4371(01)00138-8

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